6. (i)
$$\mathbf { A } = \left( \begin{array} { l l }
1 & 0
0 & 3
\end{array} \right)$$
- Describe fully the single transformation represented by the matrix \(\mathbf { A }\).
The matrix \(\mathbf { B }\) represents a rotation of \(45 ^ { \circ }\) clockwise about the origin.
- Write down the matrix \(\mathbf { B }\), giving each element of the matrix in exact form.
The transformation represented by matrix \(\mathbf { A }\) followed by the transformation represented by matrix \(\mathbf { B }\) is represented by the matrix \(\mathbf { C }\).
- Determine \(\mathbf { C }\).
(ii) The trapezium \(T\) has vertices at the points \(( - 2,0 ) , ( - 2 , k ) , ( 5,8 )\) and \(( 5,0 )\), where \(k\) is a positive constant. Trapezium \(T\) is transformed onto the trapezium \(T ^ { \prime }\) by the matrix
$$\left( \begin{array} { r r }
5 & 1
- 2 & 3
\end{array} \right)$$
Given that the area of trapezium \(T ^ { \prime }\) is 510 square units, calculate the exact value of \(k\).
| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |