For each of the following linear transformations L: R2 → R2, find a matrix representative, and then describe its effect on
(i) The x-axis;
(ii) The unit square S = (0 ≤ x, v ≤ 1):
(iii) The unit disk D = [x2 + y2 ≤ 1).
(a) Counterclockwise rotation by 45°.
(b) Rotation by 180°;
(c) Reflection in the line y = 2x;
(d) Shear along the v axis of magnitude 2;
(e) Shear along the line x = y of magnitude 3;
(f) Orthogonal projection on the line y = 2x.