Find an expression for$h\left(x\right)$.

Find the value of $a$.

By considering the image of $(0, 0)$, find $\mathit{q}$.

Hence find the angle and direction of the rotation represented by $\mathit{R}$.

Write down the matrix $\mathit{S}$.

Show that the equation of the resulting line does not depend on $m$ or $c$.

Describe fully the geometrical transformation represented by X.

Find the area of triangle X.

Find the value of $b$.

By considering the image of $(1, 0)$ and $(0, 1)$, show that

$\mathit{P}=\left(\begin{array}{cc}\frac{\sqrt{3}}{4} & \frac{1}{4}\\ -\frac{1}{4} & \frac{\sqrt{3}}{4}\end{array}\right)$.

Find the value of $a$ and the value of $b$.

Three drones are initially positioned at the points $\text{A}$, $\text{B}$ and $\text{C}$. After performing the movements listed above, the drones are positioned at points $\text{A}\prime$, $\text{B}\prime$ and $\text{C}\prime$ respectively.

Show that the area of triangle $\text{ABC}$ is equal to the area of triangle $\text{A}\prime \text{B}\prime \text{C}\prime$ .

Find ${\mathit{P}}^2$.

Find a single transformation that is equivalent to the three transformations represented by matrix $\mathit{P}$.

Write down an equation satisfied by $\left(\begin{array}{c}a\\ b\end{array}\right)$.

Use $\mathit{P}=\mathit{R}\mathit{S}$ to find the matrix $\mathit{R}$.

Write down each of the transformations in matrix form, clearly stating which matrix represents each transformation.

Find a single matrix $\mathit{P}$ that defines a transformation that represents the overall change in position.

Hence state what the value of ${\mathit{P}}^2$ indicates for the possible movement of the drone.

Find the coordinates of triangle X.

Describe fully the geometrical transformation represented by A.

Describe fully the geometrical transformation represented by B.

Find the matrix X.

Show that the points $\text{A}(1, 4), \text{B}(4, 8), \text{C}(8, 5), \text{D}(5, 1)$ form a square.

Find the area of the image of P.

Matrix A represents a combination of transformations:            

A stretch, with scale factor 3 and y-axis invariant;
Followed by a stretch, with scale factor 4 and x-axis invariant;
Followed by a transformation represented by matrix C.

Find matrix C.

Write down ${\mathit{A}}_n$, in terms of $n$.

Write down ${\mathit{A}}_1$.

Describe, in words, the effect of the transformation $T$.

Determine the area of this parallelogram.

Determine the area of this square.

Show that $\text{A' B' C' D'}$ is a parallelogram.

Hence find the area of triangle Y.

Find the coordinates of $\text{A', B', C', D'}$, the points to which $\text{A, B, C, D}$ are transformed under $T$.

Given that $T:\left(\begin{array}{c}p\\ q\end{array}\right)\mapsto 2\left(\begin{array}{c}p\\ q\end{array}\right)$, find the value of $p$ and the value of $q$.

A triangle $L$ with vertices lying on the $xy$ plane is transformed by $T$.

Explain why both $L$ and its image will have exactly the same area.