Find the canonical form for the following 2nd order surface 2. (22 + y,+ ) +5 (ay+ az+ yz) +- 2y+4z+1= 0 Write the matrix of rotation C for the canonical change of coordinates T = CE and the values (81, 82, 83) for the shift 元=十81 ý = j + 82 ミ=2+ 83

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: The image of (-2 , 5) under reflection y = -x followed by translation with translation vector (-3 ,…

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Q: Provide the mathematical expression for the sequence of rotations that transforms the frame in the…

A: In linear algebra, a Rotation matrix is a transformation matrix that is used to perform a rotation…

Q: Let A(2, -3) and B(-2,1) be vertices of a triangle ABC. If the centroid of this triangle moves on…

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Q: Let a = (- 6, 3) and b = (1, – 4). Compute the dot product.

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Q: Evaluate the Dot Product u * (v + w). If : u = (-5, 7) v = (1, 6) w = (-11, 2)

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Q: Find the image of the point A(-2, 4, 5) under a rotation of 60 degrees In the plane x = 2 about the…

A: We need to find image of given point.

Q: Find 3 different homogeneous coordinate representations for the Cartesian point (1,-2)

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Q: Select the option that gives the vector product of i+k and i + j Select one: 01 Oi+j-k Oi-j-k…

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Q: 19) Find the equation for the line in 3-space passing through the points (2,5,3) and (3, -3, 7)…

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Q: Evaluate (6x-3y)dA where Ris the parallelogram with vertices (2,0), (5,3), (6,7) and (3,4)using the…

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Q: Find the composed matrix for aligning a vector v along the unit vector j. Assume 3-D coordinate…

A: Given a vector v in the three dimensional coordinate system. And the unit vector j.   The component…

Q: Find the matrix of the mirror reflection about the x-z plane in R³.

A: Any point on the three dimension can be represented using the point: x, y, z. If the point: x, y, z…

Q: Which shape is an example of rotational symmetry?

A: Rotation symmetry is the property that a shape has exactly same look after some angle of rotation…

Q: Find the complex representation of H((-1,3),3)a, where a is the translation through i = (3, –4)

A: Given: The complex representation of H(-1,3),3), Where through

Q: Write matrix for 2D reflection about axes. Derive the transformation matrix responsible  for the…

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Q: 24 Resolveu = [8, 3, 5] into rectangular components, one of which is collinear with v = [3, 1, 2].

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Q: Locate the coordinates on the polar plane

A: Given, the points are              A2, 7π4, B-3, 5π6, C4, -π2, and D-1, -π

Q: 12) (x − 8)²(y+7)² - + 100 25 (x + 2)²_ (y − 1)² 4 64 YG X 14) = 1 G = 1

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Q: 6. Find Ar for A = and z= Az =

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Q: Which of the following describes 2D rotation? OxformMatrix.rotate(0, OxformMatrix.rotate(1,…

A: In two dimensions, the standard rotation matrix has the following form:

Q: Determine the new coordinates of the point (3,5) when the origin is moved to (2,4) by translation…

A: We have to find the point

Q: Find the scalar and vector projections of b onto a. a = (-3, -6, 2), b = (2, 1, 1) comp b= proj₂b =

A: Given that the vectors a=-3,-6,2 b=2,1,1   .