SPS SPS FM 2022 January — Question 9

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2022
SessionJanuary
TopicLinear transformations

9.
\includegraphics[max width=\textwidth, alt={}, center]{143eb5e6-a5f5-4c7b-b357-dea3fabec794-20_719_969_207_525} The diagram shows the unit square \(O A B C\) and its image \(O A ^ { \prime } B ^ { \prime } C ^ { \prime }\) under a transformation T .
  1. Write down the matrix that represents T . The transformation T is equivalent to a transformation P followed by a transformation Q . The matrix that represents \(P\) is \(\left( \begin{array} { r r } 0 & - 1
    1 & 0 \end{array} \right)\).
  2. Give a geometrical description of transformation P .
  3. Find the matrix that represents transformation Q and give a geometrical description of transformation Q .
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