Question

What transformation matrix would result in a 300 degrees counterclockwise rotation about the origin?

i cant type all of the options, but they all look like fractions inside brackets, some with square root signs.

Answer 1

the answer is B

hope this helps :)

Answer 2

For rotation by an angle, θ, in the counter-clockwise direction about the origin, the transformation matrix is given by

`\begin{pmatrix}cos\:\theta &-sin\:\theta \\ sin\:\theta &cos\:\theta \end{pmatrix}`

The given angle is θ=300°.

The values we need are

`cos\left(300^(\circ) \right)=(1)/(2)`

`sin\left(300^(\circ) \right)=-(√(3))/(2)`

Substituting these into the given transformation matrix, we have

`\begin{pmatrix}(1)/(2)&(√(3))/(2)\\ -(√(3))/(2)&(1)/(2)\end{pmatrix}`