Past exam of the mathematics course of the University of Cambridge / 2003 / ia / Paper 1 / 5B / a

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- Solution a

Solution

A positive, counterclockwise rotation takes the standard basis vectors

(1, 0)^{T}

and

(0, 1)^{T}

to

(cos θ, sin θ)^{T}

and

(- sin θ, cos θ)^{T}

. These images are the columns of its rotation matrix, so

R (θ) = (cos θ sin θ - sin θ cos θ) .

It fixes the origin, preserves the dot product and has determinant one.

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