6 [Figure 1, printed on the insert, is provided for use in this question.]
The diagram shows a rectangle \(R _ { 1 }\).
\includegraphics[max width=\textwidth, alt={}, center]{3c141dcb-4a5e-45ff-9c8e-e06762c03d10-4_652_1136_470_429}
- The rectangle \(R _ { 1 }\) is mapped onto a second rectangle, \(R _ { 2 }\), by a transformation with matrix \(\left[ \begin{array} { l l } 3 & 0
0 & 2 \end{array} \right]\).
- Calculate the coordinates of the vertices of the rectangle \(R _ { 2 }\).
- On Figure 1, draw the rectangle \(R _ { 2 }\).
- The rectangle \(R _ { 2 }\) is rotated through \(90 ^ { \circ }\) clockwise about the origin to give a third rectangle, \(R _ { 3 }\).
- On Figure 1, draw the rectangle \(R _ { 3 }\).
- Write down the matrix of the rotation which maps \(R _ { 2 }\) onto \(R _ { 3 }\).
- Find the matrix of the transformation which maps \(R _ { 1 }\) onto \(R _ { 3 }\).