Question 1180298
<pre>
Instead of doing your problem for you, I'll do one exactly like it with
different numbers.</pre>Which matrix represents the rotation of the vector (1,5) by 3pi/5 radians?<pre>
We draw the given vector:

{{{drawing(400,400,-6,3,-2,7, graph(400,400,-6,3,-2,7),

line(1,5,.8,4.8),line(1,5,1.13,4.75),

locate(.4,.4,1), locate(1.1,2.4,5),

line(0,0,1,5), green(line(0,0,1,0),line(1,0,1,5)))}}}

We calculate the length (magnitude) of the original vector by the
Pythagorean theorem:

{{{sqrt(1^2+5^2)=sqrt(1+25)=sqrt(26)=5.099019514}}}

That'll also be the magnitude of the vector after we've rotate it. 

The angle that the original vector makes with the x-axis has tangent 5/1 or 5

Make sure your calculator is in radian mode, find

tan<sup>-1</sup>(5) = 1.373400767 radians

next we add {{{(3pi)/5=1.884955592}}} to that and get 3.258356359, which
is the direction angle of the rotated vector.

We sketch in the rotated vector:

{{{drawing(400,400,-6,3,-2,7, graph(400,400,-6,3,-2,7),

   locate(.4,2.2,sqrt(26)),locate(-3.1,-.4,sqrt(26)),

line(1,5,.8,4.8),line(1,5,1.13,4.75),

locate(.4,.4,1), locate(1.1,2.4,5),

red(line(0,0,-5.064299576,-0.5940284532),

line(-4.8,-.42,-5.064299576,-0.5940284532),line(-4.7,-.7,-5.064299576,-0.5940284532)),

line(0,0,1,5), green(line(0,0,1,0),line(1,0,1,5))




)}}}

We find the horizontal component of the rotated vector by multiplying
its magnitude by the cosine of its angle.

{{{x-component = sqrt(26)cos(3.258356359)= (5.099019514)(-0.99319086) =
-5.056112587}}}

We find the vertical component of the rotated vector by multiplying
its magnitude by the sine of its angle.

{{{y-component = sqrt(26)sin(3.258356359)= (5.099019514)(-0.1164985648) =
-0.5930681439}}}

Answer, rounded off:

[-5.06,-0.59]

Now do yours exactly the same way.

Edwin</pre>