Science:Math Exam Resources/Courses/MATH152/April 2011/Question A 12
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Question A 12 

Write the matrix of the rotation which transforms to 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Either try drawing a picture or try setting up an arbitrary matrix and solving the resulting system of equations. 
Hint 2 

Rotation matrices have the form

Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. As rotation matrices are of the form
We must have that
This gives us that
or more simply
and
Thus, we plug in these values into our matrix and we see that
will do the trick. 
Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. As rotation matrices have the form
and a diagram shows that we are rotating the first vector (which is a unit vector on the positive yaxis) a total of , we have that the rotation matrix that solves our problem is
