8 The diagram below shows a rectangle \(R _ { 1 }\) which has vertices \(( 0,0 ) , ( 3,0 ) , ( 3,2 )\) and \(( 0,2 )\).
- On the diagram, draw:
- the image \(R _ { 2 }\) of \(R _ { 1 }\) under a rotation through \(90 ^ { \circ }\) clockwise about the origin;
- the image \(R _ { 3 }\) of \(R _ { 2 }\) under the transformation which has matrix
$$\left[ \begin{array} { l l }
4 & 0
0 & 2
\end{array} \right]$$
- Find the matrix of:
- the rotation which maps \(R _ { 1 }\) onto \(R _ { 2 }\);
- the combined transformation which maps \(R _ { 1 }\) onto \(R _ { 3 }\).
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