In each of the following, find the affine transformation that performs the indicated geometric operation.
(a) f: ℝ2 → ℝ2 reflects in the x-axis and then translates 3 units in the x-direction and −5 units in the y-direction.
(b) f: ℝ2 → ℝ2 rotates counterclockwise about the origin by 30 degrees and then translates −1 units in the x-direction and −3 units in the y-direction.
(c) f: ℝ2 → ℝ2 carries the points (−1, −2), (3, 1), and (−2, 4) to the points(2, 2), (0, 0), and (−3, 6).
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