For each of the following linearly dependent sets, find a redundant vector v in S and verify that $\operatorname{span}(S-\{\mathbf{v}\})=\operatorname{span}(S)$. (a) $S=\{[4,-2,6,1],[1,0,-1,2],[0,0,0,0],[6,-2,5,5]\}$, *(b) $S=\{[1,1,0,0],[1,1,1,0],[0,0,-6,0]\}$, (c) $S=\left\{\left[x_{1}, x_{2}, x_{3}, x_{4}\right] \in \mathbb{R}^{4} | x_{i}=\pm 1\right.$, for each $i \}$.

What is circulatory shock? List the five types of circulatory shock.

The temperature and Mach number before an oblique shock are $T_1=10^{\circ} \mathrm{C}$ and $M_1=3.25$, respectively, and the pressure ratio across the shock is 5 . Find the deflection angle, $\theta$, the shock angle, $\beta$, and the Mach number after the shock, $M_2$.

Why did Britain create Upper Canada and Lower Canada, and who lived in each colony?

Wendy demanded a second election because she lost to Walt in a close plurality vote. In the second election, some of Wendy's supporters voted for Walt, but Wendy managed to win. (Assume other votes stayed the same.)

Suppose that the opportunity-cost ratio for fish and lumber is $IF = IF$ in Canada but $2F = IF$ in Iceland. Then----------------should specialize in producing fish while ---------------- should specialize in producing lumber.
a. Canada; Iceland.
b. Iceland; Canada.

List the elements of the sample space defined by each experiment. Select an even single-digit whole number.

What is majority rule? When can it definitively decide an election?

For an oblique shock to occur, does the upstream flow have to be supersonic? Does the flow downstream of an oblique shock have to be subsonic?

Use the relation between work and kinetic energy given in the said exercise.
How much work is required to increase the speed of a $2000$-pound vehicle from $30\ \mathrm{mph}$ to $55\ \mathrm{mph}$?

Has the writer used a series of three or more examples in a single sentence? If so, are these examples separated by commas?

How much power is used when $600 \mathrm{~J}$ of work is done in $10 \mathrm{~s}$ ?

A supersonic airflow at

$$Ma_1 = 3.2$$

and

$$p_1 = 50 kPa$$

undergoes a compression shock followed by an isentropic expansion turn. The flow deflection is 30° for each turn. Compute

$$Ma_2$$

and

$$p_2$$

if (a) the shock is followed by the expansion and (b) the expansion is followed by the shock.

Write the fraction as a decimal.

$$\frac { 8 } { 12 }$$