If $$f(t)$$ is a finite and continuous Function for $$t \ge 0$$ the laplace transformation is given by
$$F = \int\limits_0^\infty {{e^{ - st}}\,\,f\left( t \right)dt,} $$ then for $$f(t)=cos$$ $$h$$ $$mt,$$ the laplace transformation is ___________.

Find out the eigen value of the matrix $$A = \left[ {\matrix{ 1 & 0 & 0 \cr 2 & 3 & 1 \cr 0 & 2 & 4 \cr } } \right]$$ for any one of the eigen values, find out the corresponding eigen vector?

The value of $$\int\limits_0^\infty {{e^{ - {y^3}}}.{y^{1/2}}} $$ dy is _________.

If $$H(x, y)$$ is homogeneous function of degree $$n$$ then $$x{{\partial H} \over {\partial x}} + y{{\partial H} \over {\partial y}} = nH$$