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27 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Cartesian unit vectors
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Polar coordinates Using Polar Coordinates we mark a point by how far away, and what angle it is |
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Transpose
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cause (two or more things) to exchange places transfer to a different place or context |
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er=
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er= cos θ i + sin θ j,
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eθ =
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eθ = − sin θ i + cos θ j.
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Velocity
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Velocity is speed with a direction.
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how to express i and j in terms of er and eθ |
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Speed formula |
speed = Distance/ Time |
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Speed formula with symbols
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Velocity
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Velocity formula
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sides of a right angled triangle |
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Information:- A rotation preserves distance and angle |
Information:- Any orthogonal matrix must preserve lengths and angles, since it preserves the dot product |
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Euclidean distance
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the distance between two points.
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|x| means the (Euclidean) length of vector x.
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What is the determinant? |A| means the determinant of the matrix A |
For a 2×2 matrix (2 rows and 2 columns):The determinant is:|A| = ad - bc "The determinant of A equals a times d minus b times c |
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What is the determinant of an orthogonal matrix A
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-1 or +1
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What is an orthogonal matrix
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a matrix in which two rows or two columns are vectors whose scalar product is zero
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What is a scalar product
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A scalar has only magnitude (size): 3.044, −7 and 2½ are scalarsDistance, speed, time, temperature, mass, length, area, volume, density, charge, pressure, energy, work and power are all scalars.
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What is the dot product
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The Dot Product is written using a central dot:a · bThis means the Dot Product of a and b
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How do you calculate the Dot Product of two vectors
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a · b = |a| × |b| × cos(θ)
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How to find inverse of matrix
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A matrix A that satisfies the property A^T A = I , is called .....
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An orthogonal matrix
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Information:- If the determinant of an orthogonal matrix is -1, then the matrix represents a rotated reflection |
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What is a steady state temperature?
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Temperature that does not change with time
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Inversely proportional
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is when one value decreases at the same rate that the other increases example - as speed goes up, travel time goes down. |
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Information :- proportionaly is inversely proportional to x is the same as y is directly proportional to 1/x Can be written as y=k/x |
information:-
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