Exercise 1: Applying a Scale and a Rotation Separately — Possible Solution
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GIVEN
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w = [2, -1]
S = [[3, 0], [0, 2]]
R = [[0, -1], [1, 0]]

STEP 1: APPLYING S TO w
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S w = [3(2) + 0(-1), 0(2) + 2(-1)] = [6, -2]

STEP 2: APPLYING R TO THE ORIGINAL w
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R w = [0(2) + (-1)(-1), 1(2) + 0(-1)] = [0 + 1, 2 + 0] = [1, 2]

STEP 3: VERIFYING MAGNITUDE IS PRESERVED BY THE ROTATION
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|w| = sqrt(2^2 + (-1)^2) = sqrt(4 + 1) = sqrt(5) ~= 2.236
|R w| = sqrt(1^2 + 2^2) = sqrt(1 + 4) = sqrt(5) ~= 2.236

The two magnitudes are identical, confirming this chapter's own
finding that a genuine rotation matrix never changes a vector's
length - only its direction.

WHY THIS WORKS AS AN ANSWER
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Both transformations are applied using this chapter's own matrix-
vector multiplication rule directly to the original, unmodified w
(not chained together), and the rotation result is checked against
the chapter's own length-preservation property as a way of confirming
the calculation is correct, not just performed.