 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2002/ia/paper-1/7b/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

Take positive angles counterclockwise. The rotation sends the standard basis vectors to

(cos α, sin α)

and

(- sin α, cos α)

. These images form the columns of its matrix, so

R_{2} (α) = (cos α sin α - sin α cos α) .

The columns are an orthonormal basis and the determinant is one, as required for a plane rotation.

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