Small angle rotation matrix

Questions
1

I’m trying to rotate a vector with negative coordinates by a rotation matrix with a small angle (0.030169414758875544 radians). Any idea why the X’ value is so small after rotation (-5860.53)? Is it because of the influence of the much larger Y value (-159310)? If so, how can this be fixed?

In[3]:= rotMat = RotationMatrix[0.030169414758875544]
Out[3]= {{0.999545, -0.0301648}, {0.0301648, 0.999545}}

In[2]:= point = ( {
   {-10680},
   {-159610}
  } )
Out[2]= {{-10680}, {-159610}}

In[5]:= result = rotMat.point
Out[5]= {{-5860.53}, {-159860.}}
2

The solution is correct. Size relative to circle is small. For illustrative purposes see the following.The points are plotted at bottom of circle. There is a fixed line as a reference and then gauge ‘moves’ (rotates line): note second point is around 0.03-0.04 radians.

pt1 = {-10680, -159610};

pt2 = {-5860.536872000001`, -159859.537514`};

Manipulate[Graphics[{Point[{pt1, pt2}], Circle[{0, 0},

    Norm[pt1]], Line[{{0, 0}, pt1}], 

   Line[{{0, 0}, RotationMatrix[a].pt1}]}, AxesOrigin -> {0, 0}, 

  Axes -> True],

 {{a, 0}, 0, Pi/2, AngularGauge[##, GaugeLabels -> Automatic] &}, 

 ControlPlacement -> Bottom]

wcrot.gif

3

Thanks Mark. I guess what confused me was the point was at one end of a line and the other end is at -9940, -400. Is there any way to rotate a complete 2D matrix (of arbitrary size) without having to do it on a point by point basis? I also need to skew it too, at some stage. For example:
{{ -2000, -70}, {-2340, -140}, {-2640, -30940}, {-3860, -30960}, {-4160, -62830}, {-5460, -62850}, {-5790, -94980}, {-7160, -95030}, {-7470, -127330}, {-8850, -127400}, {-9190, -159540}, {-10680, -159610} {-9940, -400},{-12940, -400}}
Thanks, Dave.

4

Sorry, I missed a comma:
{{ -2000, -70}, {-2340, -140}, {-2640, -30940}, {-3860, -30960}, {-4160, -62830}, {-5460, -62850}, {-5790, -94980}, {-7160, -95030}, {-7470, -127330}, {-8850, -127400}, {-9190, -159540}, {-10680, -159610} , {-9940, -400}, {-12940, -400}}