- The transformation \(P\) is an enlargement, centre the origin, with scale factor \(k\), where \(k > 0\) The transformation \(Q\) is a rotation through angle \(\theta\) degrees anticlockwise about the origin. The transformation \(P\) followed by the transformation \(Q\) is represented by the matrix
$$\mathbf { M } = \left( \begin{array} { c c }
- 4 & - 4 \sqrt { 3 }
4 \sqrt { 3 } & - 4
\end{array} \right)$$
- Determine
- the value of \(k\),
- the smallest value of \(\theta\)
A square \(S\) has vertices at the points with coordinates ( 0,0 ), ( \(a , - a\) ), ( \(2 a , 0\) ) and ( \(a , a\) ) where \(a\) is a constant.
The square \(S\) is transformed to the square \(S ^ { \prime }\) by the transformation represented by \(\mathbf { M }\).
- Determine, in terms of \(a\), the area of \(S ^ { \prime }\)