A = (({{3, 2}, {-1, 5}}))

VectorPlot[A.(({{x1}, {x2}})),{x1,-3,3},{x2,-3,3}]

vplot = VectorPlot[A.(({{x1}, {x2}})),{x1,-3,3},{x2,-3,3},VectorScale->{0.04,1,None}]

Eigenvectors[A]

Eigenvalues[A]

pplot = ParametricPlot[Exp[4*t]*{Cos[t]+Sin[t],Cos[t]},{t,-5,1},PlotStyle->Black]

Show[vplot,pplot]

StreamPlot[A.(({{x1}, {x2}})),{x1,-3,3},{x2,-3,3}]

Manipulate[
Plot[m*x,{x,-5,5},PlotRange->{{-5,5},{-5,5}}],
{{m,0},-5,5,Appearance->"Labeled"}
]

ParametricPlot[{2*Exp[t],Cos[t]},{t,-1,1},AspectRatio->1]