4.
$$\mathbf { A } = \left( \begin{array} { l l }
1 & 0
0 & 3
\end{array} \right)$$
- Describe the single geometrical transformation represented by the matrix \(\mathbf { A }\).
The matrix \(\mathbf { B }\) represents a rotation of \(210 ^ { \circ }\) anticlockwise about centre \(( 0,0 )\).
- Write down the matrix \(\mathbf { B }\), giving each element in exact form.
The transformation represented by matrix \(\mathbf { A }\) followed by the transformation represented by matrix \(\mathbf { B }\) is represented by the matrix \(\mathbf { C }\).
- Find \(\mathbf { C }\).
The hexagon \(H\) is transformed onto the hexagon \(H ^ { \prime }\) by the matrix \(\mathbf { C }\).
- Given that the area of hexagon \(H\) is 5 square units, determine the area of hexagon \(H ^ { \prime }\)