MHB Math Problem: Rotation on z Axis

[Coal]

I currently have a math problem that i am so thoroughly stuck on that my brain is coming out of my ears.

I am given z₁ θ = 60⁰ and R¹₀ =
[2 -2 -1]
[1 2 -2]
[2 1 2]

 

[Greg]

Hello and welcome to MHB, Coal! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?

 

[Coal]

Unfortunately the things that have been tried have been wrong from the beginning. Between the three of us there has been no real progress so any ideas are appreciated, because any positive progress is more then we have.
We apparently don't even have enough information to google how to do. It's like there is a big hole where or information should be.

 

[MarkFL]

I assume we are to compute:

$$R_z\left(60^{\circ}\right)\left[\begin{array}{c}2 & -2 & -1 \\ 1 & 2 & -2 \\ 2 & 1 & 2 \end{array}\right]=\left[\begin{array}{c}\cos\left(60^{\circ}\right) & -\sin\left(60^{\circ}\right) & 0 \\ \sin\left(60^{\circ}\right) & \cos\left(60^{\circ}\right) & 0 \\ 0 & 0 & 1 \end{array}\right]\left[\begin{array}{c}2 & -2 & -1 \\ 1 & 2 & -2 \\ 2 & 1 & 2 \end{array}\right]$$

Can you proceed with the matrix multiplication?