Solve the given systems of equations by determinants. Evaluate by expansion by minors.

$$\begin{array}{l} 2p+3r+s=4 \\ p-2r-3s+4t=-1 \\ 3p+r+s-5t=3 \\ -p+2r+s+3t=2 \end{array}$$

Do as Professor Dan Johnson does. Pour about a quarter cup of water into a gallon or 5-liter metal can with a screw top. Place the can open on a stove and heat it until the water boils and steam comes out of the opening. Quickly remove the can from the stove and screw the cap on tightly. Allow the can to stand. The steam inside condenses, which can be hastened by cooling the can with a dousing of cold water. What happens to the vapor pressure inside? (Don’t do this with a can you expect to use again.)

Find the inverse of each function. f(x) = √(2x - 3)

Simplify each expression. $-(x^2y^2)^2$

Fill in the blanks. The domain of y = cot x is all real numbers such that ________.

When 0.84 g of ZnCl2 is dissolved in 245 mL of 0.150 M NaCN, what are [Zn2+], [Zn(CN)42-], and [CN-] [Kf of Zn(CN)42- = 4.2$\times$1019]?

evaluate the sine, cosine, and tangent of the angle without using a calculator. π/3

Sketch the graph of each equation. a. $y = |x + 2|$ b. $(x + 2)^2 + y^2 = 25$ c. $(y - 3) = \log x$ d. $y = \dfrac{1}{x} + 3$

What tension in globalization is the cartoonist in source 5 attempting to capture? What kind of change over time has the cartoonist identified?

Find each product or quotient. Use significant digits. $132.5\text{ cm}\cdot43.2\text{ cm}$

Classify the function defined as even, odd, or neither.

$$\text { a. } f_{5}(x)=|x| \quad \text { b. } f_{6}(x)=\left|x+x^{3}\right|$$

Find the volume under the surface $z=x^{2}+y^{2}$ and above the square region bounded by $|x| \leq 1$ and $|y| \leq 1$.

Let V be a vector space with subspaces U and W. Prove that

$$U \cap W$$

is a subspace of V.

Arrange each set of atoms in order of increasing IE1:

Sr, Ca, Ba.