7 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { r r } 1 & - 2
2 & 1 \end{array} \right)\).
- Draw a diagram showing the unit square and its image under the transformation represented by \(\mathbf { A }\).
- The value of \(\operatorname { det } \mathbf { A }\) is 5 . Show clearly how this value relates to your diagram in part (i).
A represents a sequence of two elementary geometrical transformations, one of which is a rotation \(R\).
- Determine the angle of \(R\), and describe the other transformation fully.
- State the matrix that represents \(R\), giving the elements in an exact form.