It seems like you've uploaded an image of a mathematical problem involving a triangle transformation on the Cartesian plane. I’ll analyze it and provide a solution.

The problem seems to ask about:

1. Describing the transformation applied to triangle ABC.
2. Determining the matrix of the transformation.
3. Finding the vertices of the triangle PQR under a specific linear transformation matrix $T = \begin{bmatrix} -1 & 2 \\ 0 & 1 \end{bmatrix}$.

Analyzing the Image:

• The graph shows triangle $A'B'C'$, which is the result of a transformation applied to triangle $ABC$.
• Part (a) asks to describe the transformation (likely a rotation).
• Part (b) asks to determine the image of the triangle after the transformation.

From the handwritten notes:

• The transformation seems to be a counterclockwise rotation by 90 degrees, which aligns with the typical appearance of such a transformation.
• The matrix associated with a 90° counterclockwise rotation is: $R = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$

The linear transformation $T$, which is already given as: $T = \begin{bmatrix} -1 & 2 \\ 0 & 1 \end{bmatrix}$ will be applied to triangle $PQR$ to find the new vertices.

Next Steps:

• I'll calculate the result of applying matrix $T$ to each vertex of triangle $PQR$.
• I can also confirm the vertices of triangle $A'B'C'$ under the 90° counterclockwise rotation.

Would you like me to go ahead with these calculations and provide the solution?