In progress!
1.
2.  272 degrees
3.  two independent eigenvectors for 3. The other eigenvalue is
    +1
4. solutions spanned by exp(t), exp(-t), exp(it), exp(-it)
   or could use cos(t), sin(t) instead of last two.
5.  [ exp(t), -2exp(t)] transposed is the solution to the IVP
6.  
    A = [ ]
7.  sin(2x) = IMAG( exp(2ix)) = IMAG( exp(ix)*exp(ix))
= IMAG ( cos(x)*cos(x) -sin(x)*sin(x) + i( 2cos(x)sin(x)) )
= 2sin(x)cos(x)
8.
9. b) no - non-homogeneous case
10.