This guestion is about the geometry of SVD. Let e (3\\/@4 1/4 ) 5/4 3\\/1:"4 (1)Find an SvD of A. Namely, find 2 x 2 orthogonal matrices U, V and a diagonal matrix such that A=UZVT, T (2)Recall that every 2 x 2 matrix B defines a map Ty from R? to R? sending the point to B B Draw a picture of what happens to the unit square with vertices (g) ([1]) (3) (1) under the transformation given by the matrix 4 in this question. (3)There is an angle a [0, 27| such that if we rotate S by a (anticlockwise starting from the positive 2- axis), then the image of the rotated square under T4 becomes a rectangle R. Find @ and draw a picture of R (Hint: in the lectures the matrix Ry has determinant 1, and we know that all the orthogonal matrices of determinant 1 are of the form Ry. If in your SVD you got some orthogonal matrices of determinant 1, then you should modify it to have determinant 1 by multiplying one of the columns with 1.) (4)What is the angle (anticlockwise starting from the positive Z-axis) one needs to rotate the rectangle R by so that its legs will lie on the and y-axis