Suppose that the trace of a 2×2 matrix a is tr(a)=15 and the determinant is det(a)=50. find the eigenvalues of a.

Recall that the characteristic polynomial of a 2x2 matrix is



but and , so the characteristic polynomial for is



We're given that the trace is 15 and determinant is 50, so the characteristic polynomial for the matrix in question is



and the eigenvalues are those for which the characteristic polynomial evaluates to 0.

Answercounterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axisexplanationthe given figure has verticesrecall that for counterclockwise rotation about the origin, when we rotate figure pqrs counterclockwise through an angle of 180° about the origin, the coordinates will becomenext, we reflect in the y-axis by negating the x-coordinates of the resulting figure to obtain,therefore the correct answer is c