Question

Which matrix represents the rotation of a vector counterclockwise about the origin through an angle of 30 degrees? (A) [ 0.5

0.866
​
−0.866
0.5
​
] (B) [ 0.866
−0.5
​
0.5
0.866
​
] (C) [ 0.866
0.5
​
−0.5
0.866
​
] (D) [ 0
1
​
1
0
​
]
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Answer 1

(B)

`\left[\begin{array}{cc}0.866&-0.5\\0.5&0.866\end{array}\right]`

Explanation:

You want the rotation matrix for rotation 30° counterclockwise about the origin.

Rotation matrix

For a rotation of positive angle θ (counterclockwise) about the origin, the transformation matrix is ...

`\left[\begin{array}{cc}cos((\theta))&-sin((\theta))\\sin((\theta))&cos((\theta))\end{array}\right]`

For θ = 30°, this is ...

`\boxed{\left[\begin{array}{cc}0.866&-0.5\\0.5&0.866\end{array}\right]}`

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