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# 2-by-2 rotation matrix watch

1. Vb
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2. (Original post by Deeboss)
QUESTION 19)

Ok so this is the following method I have used.

2D vector v rotated by 2x2 rotation matrix R will be the 2D vector v' as follows:
v' = R v
2x2 rotation matrix R is as follows, where is the rotation angle.

My answer was.

R = 3.76 -11.28 (2.dp)
19.73 7.52

Sorry about my terrible 2x2 matrix above, I dont know how to use the actual symbols on student room. Please check my answer and let me know!

R12 = -11.28?
Your answer doesn't seem to have anything to do with the question. The elements of the matrix, including r12, will all be values between -1 and 1 inclusive.
3. (Original post by ghostwalker)
Your answer doesn't seem to have anything to do with the question. The elements of the matrix, including r12, will all be values between -1 and 1 inclusive.
How do you work out they will all be values between -1 and 1? What is your method?
4. (Original post by Deeboss)
How do you work out they will all be values between -1 and 1? What is your method?
A rotation matrix consists of sines and cosines, hence their value must be between -1 and 1. You actually have it in your first post!
5. (Original post by ghostwalker)
A rotation matrix consists of sines and cosines, hence their value must be between -1 and 1. You actually have it in your first post!
I dont understand then? How is my answer wrong? -sin (70 degrees) x 12 = -11.28 (2.dp) Wouldnt this be the value for element r12 to 2.dp?

Again sorry I dont mean to sound like I am right or wrong just trying to get my head around this
6. (Original post by Deeboss)
I dont understand then? How is my answer wrong? -sin (70 degrees) x 12 = -11.28 (2.dp) Wouldnt this be the value for element r12 to 2.dp?

Again sorry I dont mean to sound like I am right or wrong just trying to get my head around this
Why are you multiplying it by 12?

is the name of the element in row 1, column 2.
7. (Original post by ghostwalker)
Why are you multiplying it by 12?

is the name of the element in row 1, column 2.
Well if there is no value to the r12 element how do I work that out? What do I multiply -sin70 by?
8. (Original post by Deeboss)
Well if there is no value to the r12 element how do I work that out? What do I multiply -sin70 by?
You don't need to multiply it by anything.

The question is asking you to find the value of the element in row1 column2 of the matrix. They call that element

It's standard terminology for the elements of a matrix to have two subscripts; the first refers to the row and the second to the column.
9. (Original post by ghostwalker)
You don't need to multiply it by anything.

The question is asking you to find the value of the element in row1 column2 of the matrix. They call that element

It's standard terminology for the elements of a matrix to have two subscripts; the first refers to the row and the second to the column.
Ohhh okaay. So it would only just be -sin 70? Which gives me an answer to -0.94 (2.dp)
10. (Original post by Deeboss)
Ohhh okaay. So it would only just be -sin 70? Which gives me an answer to -0.94 (2.dp)
is that correct ghostwalker? My most previous post?
11. (Original post by Deeboss)
is that correct ghostwalker? My most previous post?
Yep.
12. (Original post by ghostwalker)
Yep.
Dude, regardless of the work. I just wanted to say thanks for helping me out with this. Have a great week bro.

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