 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ia/paper-1/8a/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Direct multiplication and the identities

cos^{2} θ + sin^{2} θ = 1

and

cosh^{2} θ - sinh^{2} θ = 1

give

R R^{T} = I, S J S = J, J = (10 0 - 1) .

Thus $R$ is an orthogonal matrix, while $S$ preserves the indefinite quadratic form $x_{1}^{2} - x_{2}^{2}$ .

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