Question 857574
Use the dot product,
{{{U*V=abs(U)abs(V)cos(theta)}}}
{{{cos(theta)=(U*V)/(abs(U)abs(V))}}}
The dot product is 
{{{U*V=-2*-3+-1*1=6-1=5}}}
{{{abs(U)=sqrt((-2)^2+(-1)^2)=sqrt(5)}}}
{{{abs(V)=sqrt((-3)^2+(1)^2)=sqrt(10)}}}
So then,
{{{cos(theta)=(5)/sqrt(50)}}}
{{{cos(theta)=sqrt(25)/sqrt(50)}}}
{{{cos(theta)=sqrt(1/2)}}}
{{{cos(theta)=sqrt(2)/2}}}
{{{theta=45}}}