In $(\mathbb{Z}_{25}^*,\otimes)$ the set H={1,6,11,16,21} is a subgroup. Find the equivalence classes of the congruence mod H relation.

Answer for the sequence $v$ defined by $v_n=n!+2$, $n\geq 1$. Find $\sum_{i=1}^4 v_i$.

What are rituals? How do rituals help a species' survival?

Make a table that lists the characteristics of seedless vascular plant groups.

If

$$\overrightarrow{\mathrm{AB}}=\left( \begin{array}{c}{-1} \\ {3} \\ {2}\end{array}\right), \overrightarrow{\mathrm{AC}}=\left( \begin{array}{c}{2} \\ {-1} \\ {4}\end{array}\right)$$

, and

$$\overrightarrow{\mathrm{BD}}=\left( \begin{array}{c}{0} \\ {2} \\ {-3}\end{array}\right)$$

, find: $\overrightarrow{\mathrm{CD}}$

Imagine you are a molecular-sized reporter and are able to witness a chemical reaction achieve chemical equilibrium. Write down what you observe. Be sure to describe the actions of the reactants and products, and the setting!

What are three ways the body loses water?

Using Lagrange’s theorem, find the orders of all the potential subgroups of the following groups:

a. G = <Z$_{18}$, +>

b. G = <Z$_{29}$, +>

c. G = <Z$_{12}$*, $\times$>

d. G = <Z$_{19}$*, $\times$>

What is the 3rd person plural imperfect subjunctive of the verb 'poder' ?

If $\cos \theta=-\frac{3}{4}, \frac{\pi}{2}<\theta<\pi$ find the exact value of: $\sin (\theta+\pi)$

If you could break food down into its components, what would you find?

Read the editorial carefully. Use the tips for analyzing an editorial to help you answer the questions below. ATTITUDES TOWARD WATER RESTRICTIONS: Action on Tuesday by the State Water Resources Control Board to restrict lawn watering and home car-washing... barely raised eyebrows in-state. That's because most urban agencies had already imposed those kinds of limits more than a year ago. Californians responded initially with big water savings but let the hoses and sprinklers run again toward the end of last year, as the Sierra snow began to fall... This winter was a bit wetter than last, but that's not saying much. There has been too little precipitation to replenish the reservoirs and aquifers that water users have been drawing down during the dry times. There's enough water for the coming year and the year after that besides - but not at the current rate of use, and certainly not if wet winters don't resume. Stored water is a kind of bank account meant to get users through an arid year or two, but it cannot be expected to preserve the state through an extended drought like one that afflicted Australia for a decade and a half beginning in the 1990 s... In this fourth year of drought here. Californians must begin using water as though they are still at the front end of that sort of cataclysm. Australia responded to the so-called millennium drought by permanently changing the way it produces and delivers water... California has dabbled in such things for decades, but it's now evident that the state must do Australian-style rethinking and move quickly to Australia-style action. Source: Los Angeles Times. How would you frame a response to this editorial? What points would you make and how would you support them?

a. What six steps are required to open a general ledger account? b. List the steps in the posting process.

Find the rank of $\lambda I-A$ for each eigenvalue by row reduction, and use the results to show that A is diagonalizable.

$$A=\left[\begin{array}{rrr}{0} & {-1} & {1} \\ {-1} & {0} & {1} \\ {1} & {1} & {0}\end{array}\right]$$

.