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Orienting boundary with surface | Multivariable Calculus | Khan Academy

Video vocabulary

normal

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US / 'nɔ:ml /

UK / ˈnɔrməl /

A1
  • adjecitve
  • Standard or regular way of doing something
  • Having standard mental or physical ability, health

itself

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US / ɪtˈself /

UK / ɪtˈsɛlf /

A1
  • pronoun
  • Referring to it

once

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US / wʌns /

UK / wʌns /

A1
  • adverb
  • One time; one instance
  • At a time in the past
  • conjunction
  • When; as soon as

inside

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US / ˌɪn'saɪd /

UK / ɪnˈsaɪd, ˈɪnˌsaɪd /

A2
  • adjecitve
  • Being in something
  • Being in a building
  • adverb
  • Into a house; indoors
  • noun
  • Inner part or surface of something

point

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US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

valley

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US / 'vælɪ /

UK / ˈvæli /

A2
  • noun
  • Area between mountains with river running through

sure

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US / ʃʊə(r) /

UK / ʃʊr /

A1
  • adjecitve
  • Having no doubts about something
  • Have confidence in your own words or actions
  • Firmly established or held; being firm or stable
  • Being correct or true
  • adverb
  • What you say to agree willingly

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

walk

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US / wɔ:k /

UK / wɔk /

A1
  • noun
  • Journey on foot done for pleasure or exercise
  • verb
  • To move with your legs at a slowish pace

convention

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US / kənˈvenʃn /

UK / kənˈvɛnʃən /

A2
  • adjecitve
  • Concerning a large formal assembly or meeting
  • noun
  • Official agreement between two or more countries
  • Large formal assembly, e.g. to make laws
  • Proper and widely accepted way of behaving

true

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US / tru: /

UK / tru: /

A1
  • adjecitve
  • Agreeing with the facts; not false; real or actual

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

understand

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US / ˌʌndə'stænd /

UK / ˌʌndɚˈstænd /

A1
  • verb
  • To know the meaning of language, what someone says

pick

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US / pɪk /

UK / pɪk /

A1
  • noun
  • Sharp tool used for breaking the ground
  • Item selected from a group of choices
  • verb
  • To take fruit or vegetables from a plant or tree
  • To decide on a thing from various choices; select
  • To remove (flower, etc.) with your fingers

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

maybe

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US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

yellow

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US / ˈjeləʊ /

UK / ˈjeloʊ /

A1
  • adjecitve
  • Color of lemons or the sun
  • Lacking in courage; cowardly (used as an INSULT)
  • verb
  • To turn yellow, often due to being old

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

vector

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US / 'vektə(r) /

UK / ˈvɛktɚ /

B2
  • noun
  • Math a quantity that has both size and direction

inward

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US / ˈɪnwəd /

UK / ˈɪnwərd /

B1
  • adverb
  • At the inside of

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

restate

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US / ˌri:ˈsteɪt /

UK / riˈstet /

C1
  • verb
  • To repeat differently to ensure understanding

hat

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US / hæt /

UK / hæt /

A1
  • noun
  • Item of clothing worn on your head

visualize

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US / ˈvɪʒuəlaɪz /

UK / ˈvɪʒuəˌlaɪz /

B1
  • verb
  • To create a picture in your mind of something

outward

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US / ˈaʊtwəd /

UK / ˈaʊtwəd /

B1
  • adjecitve
  • Going away from a place that will be returned to
  • Seeming to be from the outside
  • Concerning how something appears on the outside

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

video

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US / 'vɪdɪəʊ /

UK / ˈvɪdiˌo /

A2
  • adjecitve
  • Of a moving film, with sound
  • noun
  • Recording capturing action with sound
  • verb
  • To make a moving film of, with sound

stoke

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US / stəʊk /

UK / stok /

C1
  • verb
  • To add fuel or tend a fire to make it stronger

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

surface

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US / 'sɜ:fɪs /

UK / ˈsɚfəs /

A2
  • adjecitve
  • Of the top layer; not deep or meaningful
  • noun
  • Top layer of the ground or of water
  • Nature or emotions that show, but may not be true
  • Outside or upper layer of something
  • verb
  • To give (road) a top layer
  • To appear after being hidden, unseen, or unknown
  • To come to the top of something; emerge
  • To come to the top level of water, mud, etc.

upside

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US / ˈʌpsaɪd /

UK / ˈʌpˌsaɪd /

A2
  • noun
  • Above, over
  • A positive aspect; advantage

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

sal

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US / sæl /

UK / sæl /

A1
  • noun
  • A North Indian tree that yields hard, durable timber and dammar resin.

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

kind

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US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

also

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US / 'ɔ:lsəʊ /

UK / ˈɔlso /

A1
  • adverb
  • In addition; too; in a similar way

bowl

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US / bəʊl /

UK / bol /

A2
  • noun
  • Part of an object that has a rounded, inward curve
  • Round container used for holding rice, soup etc.
  • Round Building to watch sports events, concerts
  • Low-lying land with higher ground around it
  • verb
  • To roll a ball in the sport of bowling
  • To throw a ball in a game such as cricket

order

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US / 'ɔ:də(r) /

UK / ˈɔrdɚ /

A1
  • noun
  • Religious or social group, as of nuns
  • Instructions to others to do what you want
  • State in which things are neat and organized
  • What you ask to buy, e.g. food in restaurant
  • Social or political control of an area
  • verb
  • To put things in a sequence, e.g. a, b, c
  • To give instructions to others to do what you want
  • To ask for something you want to buy, e.g. a meal

path

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US / pɑ:θ /

UK / pæθ, pɑθ /

A2
  • noun
  • Method of living leading to a particular result
  • Track made with stones, by walking over the ground

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

hill

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US / hɪl /

UK / hɪl /

A2
  • noun
  • High land not as high as a mountain
  • Where the road or land goes upward; slope
  • Person's name

differently

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US / 'dɪfrəntlɪ /

UK / ˈdɪfərəntlɪ /

A2
  • adverb
  • In another and different manner

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

might

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US / maɪt /

UK / maɪt /

A1
  • other
  • Used to politely request an action
  • Used to express that something could happen
  • Power, strength, force or influence

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

big

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US / bɪɡ /

UK / bɪɡ /

A1
  • adjecitve
  • Popular
  • Serious
  • Large

opposite

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US / ˈɔpəzit /

UK / ˈɑpəzɪt /

A2
  • adjecitve
  • Being totally different from
  • noun
  • Person, thing that is totally different to another
  • preposition
  • Across from or on the side facing something

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

essentially

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US / ɪˈsenʃəli /

UK / ɪˈsenʃəli /

A2
  • adverb
  • Basically; (said when stating the basic facts)

type

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US / taɪp /

UK / taɪp /

A1
  • noun
  • Printed letters or blocks used for printing them
  • Group of things or people sharing common features
  • verb
  • To identify something belonging to a group
  • To write by touching keys on a keyboard

boundary

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US / 'baʊndrɪ /

UK / ˈbaʊndəri, -dri /

B1
  • noun
  • A division or border to separate two areas

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

down

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US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

each

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US / i:tʃ /

UK / itʃ /

A1
  • determiner
  • Every one of two or more things
  • pronoun
  • Per one person or thing

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

again

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US / ə'ɡen /

UK / əˈɡɛn /

A1
  • adverb
  • One more time, once more

about

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US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

hard

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US / hɑ:d /

UK / hɑː(r)d /

A1
  • adjecitve
  • Difficult to do; difficult to understand
  • (Of facts) not able to be misunderstood; clear
  • (Of alcohol) strong
  • Involving or requiring lots of work, effort, care
  • Being full of pain, trouble, and problems
  • Strong
  • (Of edge) clear; sharp
  • Difficult to bend, break or cut; solid
  • adverb
  • With lots of force, power, or impact

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

wear

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US / weə(r) /

UK / wer /

A1
  • noun
  • Clothing designed for a purpose e.g. skiing
  • Damage from continual use over a long period
  • verb
  • To have clothes, glasses, shoes etc. on your body
  • To display an expression or emotion on the face
  • To become weaker or damaged from continued use

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

theorem

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US / ˈθɪərəm /

UK / ˈθiərəm, ˈθɪrəm /

B2
  • noun
  • A statement that can be proved

mind

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US / maɪnd /

UK / maɪnd /

A1
  • noun
  • One's opinion or way of thinking about something
  • Part of humans that allows us to think or feel
  • verb
  • To be bothered or upset by something
  • To take care of someone e.g. as a bodyguard

draw

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US / drɔ: /

UK / drɔ /

A1
  • noun
  • Something that attracts people to visit a place
  • A lottery or prize
  • Result of a game, contest where the score is equal
  • verb
  • To attract attention to someone or something
  • To get closer to or approach something or someone
  • To influence a person's involvement in something
  • To move an object by pulling
  • To create an image using pen or pencil and paper
  • To take one thing out of a container, etc.
  • (Of 2 teams) to finish a game with the same score

dip

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US / dɪp /

UK / dɪp /

B1
  • noun
  • Food or sauce eaten with crackers/raw vegetables
  • Place on surface (e.g. a road) lower than the rest
  • verb
  • To decrease or lower temporarily
  • To put something in and out of a liquid quickly
  • To switch off or lower lights on a car

contour

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US / 'kɒntʊə(r) /

UK / ˈkɑnˌtʊr /

C2
  • noun
  • Shape of the outside edge of a face, a hill, etc.

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

keep

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US / ki:p /

UK / kip /

A1
  • noun
  • Large, strong tower in the middle of a castle
  • Money spent on you so you can live in a place
  • verb
  • To continue doing something; not to stop
  • To stop balls going in a goal in sports
  • To not give back or return something
  • (Of food) to not spoil or not rot
  • To take possession of something to own, e.g. a pet
  • To have and continue to hold something
  • To do something that you have promised or agreed
  • To stay in a certain place or condition
  • To maintain the rules

base

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US / beɪs /

UK / bes /

A2
  • noun
  • Place military personnel live, train, and operate
  • Bottom part of an object that touches a surface
  • Unit of counting, e.g. 10 for counting
  • Most important idea or ingredient to add others
  • Origin or start from which something came
  • Main place where an organization or a person works
  • verb
  • To use as the starting point or origin for
  • To have as the main location for (company, etc.)

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

put

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US / pʊt /

UK / pʊt /

A1
  • phrasal verb
  • to make a light stop shining by pressing or moving a switch
  • verb
  • To move or place a thing in a particular position
  • To rate something in importance or value
  • To write or say something in a certain manner

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

along

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US / əˈlɒŋ /

UK / əˈlɔ:ŋ /

A1
  • adverb
  • As a companion; taken with someone
  • preposition
  • At a point on a line

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

think

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US / θɪŋk /

UK / θɪŋk /

A1
  • verb
  • To have an idea about something without certainty
  • To have an idea, opinion or belief about something

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

head

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US / hed /

UK / hɛd /

A1
  • noun
  • Counter for the number of cattle
  • Natural mental ability or intelligence
  • Leader or person with the greatest authority
  • Mind; mental ability; mental state
  • Side of a coin with a head on it
  • Top part of your body with eyes and a mouth
  • Starting point of something, e.g. a river
  • verb
  • To hit a ball with your head in a game
  • To be first or at the front or top (e.g. a list)
  • To travel or move toward a particular place; To go in a particular direction
  • To become the leader of something
  • To lead or be responsible for something

traverse

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US / trəˈvɜ:s /

UK / trəˈvɜ:rs /

B2
  • verb
  • To pass across, over, or through

positive

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US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

clockwise

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US / ˈklɒkwaɪz /

UK / ˈklɑkˌwaɪz /

B1
  • adjecitve
  • In the same direction as a clock's hands

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

orient

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US / 'ɔ:rɪənt /

UK / ˈɔriənt, -ˌɛnt, ˈor- /

B1
  • noun
  • Area comprising Asia
  • verb
  • To give information about something to newcomers

pop

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US / pɒp /

UK / pɑp /

B2
  • adjecitve
  • Type of music or art popular with many people
  • noun
  • Sweet soda drink
  • verb
  • To cause something to open or burst suddenly
  • To go to or in a place for a brief period of time

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

situation

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US / ˌsɪtʃuˈeɪʃn /

UK / ˌsɪtʃuˈeʃən /

A1
  • noun
  • Place, position or area that something is in
  • Circumstance or condition surrounding an event
  • An unexpected problem or difficulty

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

look

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US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

counterclockwise

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US / ˌkaʊntəˈklɒkwaɪz /

UK / ˌkaʊntərˈklɑ:kwaɪz /

A1
  • other
  • In a direction opposite to the direction in which the hands of a clock move
  • In the direction opposite to the rotation of the hands of a clock

way

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US / weɪ /

UK / we /

A1
  • adverb
  • Used to emphasize the amount of something
  • noun
  • Particular aspect of something being thought about
  • One of various choices that could be made
  • Particular existing condition or state
  • (Often long) distance or length of time
  • How something is done
  • Route to go to a place
  • Small street
  • Usual behavior, emotions or habits of someone

direction

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US / də'rekʃn /

UK / dɪˈrɛkʃən, daɪ- /

A2
  • noun
  • When someone tells people what to do
  • Describes the way you are going, e.g. North

orientation

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US / ˌɔ:riənˈteɪʃn /

UK / ˌɔriɛnˈteʃən, -ən-, ˌor- /

B1
  • noun
  • Where you are in a location, e.g. facing east/west
  • Process of giving information about something new
  • A person's preferences, e.g. sexual preferences

top

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US / tɒp /

UK / tɑp /

A1
  • adjecitve
  • Being good or great; excellent
  • Being the most in degree or quality
  • noun
  • Item of clothing covering shoulders to waist, hips
  • A cover or lid
  • Part (e.g. road) that is the furthest away
  • Highest or upper part or point of something
  • Best or highest status or position
  • Flat upper surface or edge of an object
  • Child's toy that spins on its point
  • Upper section or leaves of fruits and vegetables
  • Winning in a sport or contest
  • verb
  • To be higher or larger than a specific value
  • To arrive at the highest point of something
  • To put a cover or layer or over something
  • To kill; murder
  • To hold the highest position on a list
  • To be more important, successful or better than
  • To beat someone or win at a game

correctly

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US / kə'rektlɪ /

UK / kəˈrɛktlɪ /

A2
  • adverb
  • In an accurate or correct manner
  • Subtitles section
  • I've restated Stokes' theorem.
  • And what I want to do in this video is make sure that we get our orientation right.
  • Because when we think about a normal vector to a surface there are actually two normal vectors.
  • There-- based on the way I've drawn it right over here, there could be the one that might pop outward, like this.
  • Or there might be the one that pops inward, just like that.
  • Both of those would be normal to the surface right there.
  • And also, when we think about a path that goes around the boundary of a surface, there's two ways to think about that path.
  • We could be going-- based on how I've oriented it right now, we could go in a counterclockwise orientation, or direction.
  • Or we could go in a clockwise orientation, or direction.
  • So in order to make sure we're using Stokes' theorem correctly, we need to make sure we understand which each convention it is using.
  • And the way we think about it is, whatever the normal direction we pick-- and so let's say we pick this normal direction right over here, the one I am drawing in yellow.
  • So if we pick this as our normal vector.
  • So we're essentially saying maybe that's the top, one way of doing it is, that's the top of our surface, then the positive orientation that we need to traverse the path in is the one that if your head was pointed in the direction of the normal vector,
  • and you were to walk along that path, the inside, or the surface itself would be to your left.
  • And so, if my head is pointed in the direction of the normal vector-- so this is me right over here-- my head is pointed in the direction of the normal vector-- I'm wearing a big arrow hat right over there-- and if I'm walking around the boundary,
  • the actual surface needs to be to my left.
  • So I need to be-- this is me walking right over here-- I need to be walking in the counterclockwise direction just like that.
  • Then that's the convention that we use when we're thinking about Stokes' theorem.
  • If oriented this thing differently, or if we said that no, no, no, no, no, this is not the normal vector.
  • This is not the, essentially, the top that we want to pick.
  • If we wanted to pick it the other way, if we wanted to go in that direction, If we wanted that to be our normal vector, in order to be consistent, we would have to now do the opposite.
  • I would now have to have my head going in that direction.
  • And then I would have to walk, once again, and this might be a little bit harder to visualize.
  • I would have to walk in the direction that the surface is to my left.
  • And now, in this situation, instead of the surface looking like a hill to me, the surface would look like some type of a bowl, or some type of a valley or something like that to me.
  • And the way that I would have to do it now, and it's a little bit hard to visualize the upside down Sal, but the upside down Sal would have to walk in this direction in order for the bowl, or the dip, to be to my left.
  • So that's just important to keep this in mind in order for this to be consistent with this right over here.
  • Put your head in the direction of the normal vector.
  • Or you can kind of view that as the top of the direction that the top of the surface is going in.
  • And then the contour, or the direction that you would have to traverse the boundary in order for this to be true, is the direction with which the surface is to your left.