Question

Write the inverse of the matrix $\left(\begin{array}{l l }cosθ & -sinθ \\ sinθ & cosθ\end{array}\right)$ .

Find a unit vector parallel to the sum of vectors $\stackrel{\wedge}{i}+\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +5\stackrel{\wedge}{k}$

Evaluate $\textstyle\int\!{\frac{x^{3}-x^{2}+x-1}{x-1}}\,d x\,.$

If A is a square matrix of order 3 such that $|a d j\,A|$ = 225, find $|A^{\prime}|.$

If $\left(\begin{array}{l l }2x & 3\end{array}\right)$ $\left(\begin{array}{l l }1 & 2 \\ -3 & 0\end{array}\right)$ $\left(\begin{array}{l }x \\ 3\end{array}\right)$ = 0,

For what values of $\stackrel{\rightarrow}{a}\$, the vectors $2\stackrel{\wedge}{i}-3\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$ and $a\,{\hat{\boldsymbol{i}}}+6\,{\hat{\boldsymbol{j}}}-8\,{\hat{\boldsymbol{k}}}$ are collinear?

If f(x) = 27x³ and g(x) = $x^{1/3}$, then find gof(x).