Why is identifying the frame of reference important in describing motion?

Find the equation of the following quadric surface

$$x^{2}+3y^{2}+3z^{2}+4xy+4xz=60$$

relative to principal axes.

Use a calculator to determine whether each statement is true or false. If the statement is true, explain why this is so using one of the rules of divisibility the table.

$$\begin{matrix} \text{Divisible By} & \text{Test} & \text{Example}\\ \text{2} & \text{The last digit is 0, 2, 4, 6, or 8.} & \text{5,892,796 is divisible by 2 because the last digit is 6.}\\ \text{3} & \text{The sum of the digits is divisible by 3.} & \text{52,341 is divisible by 3 because the sum of the digits is 5+2+3+4+1=15, and 15 is divisible by 3.}\\ \text{4} & \text{The last two digits form a number divisible by 4.} & \text{3,947,136 is divisible by 4 because 36 is divisible by 4.}\\ \text{5} & \text{The number ends in 0 or 5.} & \text{28,160 and 72,805 end in 0 and 5, respectively. Both are divisible by 5.}\\ \text{6} & \text{The number is divisible by both 2 and 3. (In other words, the number is even and the sum of its digits is divisible by 3.)} & \text{954 is divisible by 2 because it ends in 4. 954 is also divisible by 3 because the digit sum is 18, which is divisible by 3. Because 954 is divisible by both 2 and 3, it is divisible by 6.}\\ \text{8} & \text{The last three digits form a number that is divisible by 8.} & \text{ 593,777,832 is divisible by 8 because 832 is divisible by 8.}\\ \text{9} & \text{The sum of the digits is divisible by 9.} & \text{5346 is divisible by 9 because the sum of the digits, 18, is divisible by 9.}\\ \text{10} & \text{The last digit is 0.} & \text{998,746,250 is divisible by 10 because the number ends in 0.}\\ \text{12} & \text{The number is divisible by both 3 and 4. (In other words, the sum of the digits is divisible by 3 and the last two digits form a number divisible by 4.)} & \text{614,608,176 is divisible by 3 because the digit sum is 39, which is divisible by 3. It is also divisible by 4 because the last two digits form 76, which is divisible by 4. Because 614,608,176 is divisible by both 3 and 4, it is divisible by 12.}\\ \end{matrix}$$

$$5 | 38,814$$

Find an equation for

$$f ^ { - 1 } ( x )$$

Then graph f and

$$f ^ { - 1 }$$

in the same rectangular coordinate system.

$$f ( x ) = 1 - x ^ { 2 } , x \geq 0$$

a. Find the value of these expressions when a = 2 and b = 4. (i) 2a + b $\text { (ii) } 2(a+b) \quad \text { (iii) } \quad a^{2}-b^{2} \quad \text { (iv) }(a-b)^{2}$ b. State whether your answers to part a are natural numbers or not.

Write a biconditional for the following conditional. What is its truth value?

It two lines intersect at right angles, then they are perpendicular.

Would you expect to find free oxygen gas in the atmospheres of the giant planets? Why or why not?

Which of the following would be a more humid area: the Sahara Desert on a cold night or the Florida coast on a warm day?

Rewrite each of the following sentences, correctly using underlining (italics), quotation marks, and ellipses. Be careful to show the correct position of quotation marks in relation to other punctuation.

Do not rush into anything, Leroy warned, that you are not willing to finish.

Which spinal region includes the vertebrae of the neck? A. thoracic, B. lumbar, C. sacral, D. cervical.

Two rings of radius 5 cm are 20 cm apart and concentric with a common horizontal axis. The ring on the left carries a uniformly distributed charge of $+35 \mathrm{nC}$, and the ring on the right carries a uniformly distributed charge of $-35 \mathrm{nC}.$ If a charge of $-5 \mathrm{nC}$ were placed midway between the rings, what would be the magnitude and direction of the force exerted on this charge by the rings?

On a separate sheet of paper, answer the questions below. Make sure you read carefully and answer all parts of the questions. What is the theory of mercantilism? What did the governments of European nations do to encourage exports and favorable trade balances?

Given a function f defined and having a finite derivative in (a, b) and such that $\lim _{x \rightarrow b-} f(x)=+\infty$. rove that $\lim _{x \rightarrow b-} f^{\prime}(x)$ either fails to exist or is infinite.

Use Part I of the Fundamental Theorem to compute each integral exactly. $\int_{0}^{t}\left(\sin ^{2} x+\cos ^{2} x\right) d x$