Figure 1: In this case, 3' = (1,0) and 3' = (0,1) are both rotated by 9 = g in _5 is _; T Show that U = i g and VT = '1' 3 are both rotation matrices, and 2 2 5 2 nd their corresponding rotational angles EU and 6m. (iii) Give an explanation for all geometric transformations performed by the SVD of A. In what order are the transformations performed? (iv) The unit circle shown in Figure 2 has been transformed by a number of different 2D transformations. The transformation results are shown in Figure 3. I-1.5 -1.0 -O.5 0.0 0'5 10 1.5 Figure 2: unit circle and plane basis ?, ? 1.5 1.0 1.0 0.5 0.5 00 0.0 -0.5 -0-5 w10 7, -10 45-15 -1.0 -o.5 0.0 0.5 10 15 45-15 -1.0 -0.5 0.0 0.5 10 15 (a) (b)