When serving as a ceremonial figure representing the United States, the president is fulfilling which presidential role?

The “Necessary and Proper” clause of the Constitution is sometimes called the _______ clause.

Discuss at least three ways of increasing voter turnout.  Which way do you think would be most effective?  Explain your answer. (3 points)

Use the Wronskian to show that the set \(\left\{3x,x^{2},\sin\left(x\right)\right\}\) is linearly independent in \(C^{\infty}\left(-\infty,\infty\right)\).

After the House votes to pass a bill, it becomes law.

Let \(\mathcal{B}=\left\{\begin{bmatrix}4\\-1\end{bmatrix},\begin{bmatrix}7\\-2\end{bmatrix}\right\}\) and \(\mathcal{B}^{\prime}=\left\{\begin{bmatrix}5\\4\end{bmatrix},\begin{bmatrix}1\\1\end{bmatrix}\right\}\). Find the transition matrix \(P_{\mathcal{B}\to\mathcal{B}^{\prime}}\).

Which style of journalism is based on facts and describes newsworthy events at the local, national or international level?

Given the following matrix \(A\) and its rref, find bases for \(\text{row}\left(A\right), \text{col}\left(A\right),\) and \(\text{null}\left(A\right)\). Also, state the rank and nullity of \(A\). \[A=\begin{bmatrix}2&1&-1&0&3&8&3\\3&1&-3&3&-8&19&7\\-1&1&5&-2&8&-11&-2\\-1&1&5&1&1&20&6\end{bmatrix}\] \[\text{rref}\left(A\right)=\begin{bmatrix}1&0&-2&0&1&5&1\\0&1&3&0&1&-2&1\\0&0&0&1&-4&2&1\\0&0&0&0&0&0&0\end{bmatrix}\]

Let \(f\) be the transformation of \(\mathbb{R}^{2}\) given by rotating \(70^{\circ}\) counterclockwise around the origin. Find the standard matrix for \(f\) and then use that to find where the point \(\left(4,4\right)\) gets sent under this rotation. (As \(70^{\circ}\) is not a special angle, you will have to use decimal approximations.)

In what basic way can all people influence public policy?