Construct the general solution of x'=Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories.

$$A=\left[ \begin{array}{rrr}{30} & {64} & {23} \\ {-11} & {-23} & {-9} \\ {6} & {15} & {4}\end{array}\right]$$

Explain how a cell's DNA can limit the cell's size.

Use an appropriate coordinate system to find the volume of the given solid. The solid below $z=\sqrt{x^{2}+y^{2}}$, above the xy-plane and inside $x^{2}+y^{2}=4$

Define (a) harambee, (b) pyrethrum, (c) malnutrition.

The short-term (no more than 24 hours) parking fee F (in dollars) for parking x hours at O’Hare International Airport’s main parking garage can be modeled by the function

$$F(x)=\left\{\begin{array}{ll}{3} & {\text { if } 0<x \leq 3} \\ {5 \text { int }(x+1)+1} & {\text { if } 3<x<9} \\ {50} & {\text { if } 9 \leq x \leq 24}\end{array}\right.$$

Determine the fee for parking in the short-term parking garage for 15 hours

How is a nation's level of development defined?

Evidence of words’ subtle influence on thinking best supports the notion of a. Wernicke’s area. b. Broca’s area. c. linguistic determinism. d. babbling. e. aphasia.

A point on the terminal side of an angle $\theta$ in standard position is given. Find the exact value of each of the six trigonometric functions of $\theta.$ (-1,1)

Revere Water Company reported the following items on its statement of shareholders’ equity for the year ended December 31, 2012:

$$\begin{matrix} & \text{\$3.50 Par Common Stock} & \text{Additional Paid-in Capital} & \text{Retained Earnings} & \text{Accumulated Other Comprehensive Income} & \text{Total Shareholders’ Equity}\\ \text{Balance, December 31, 2011............. } & \text{\$395} & \text{\$1,505} & \text{\$4,700} & \text{\$8} & \text{\$6,608}\\ \text{Net earnings...................................... } & \quad & \quad & \text{1,050}\\ \text{Other comprehensive income............} & \quad & \quad & \quad & \text{1}\\ \text{Issuance of stock............................... } & \text{140} & \text{70}\\ \text{Cash dividends.................................. } & \quad & \quad & \text{(80)}\\ \text{Balance, December 31, 2012.............}\\ \end{matrix}$$

Determine the December 31, 2012, balances in Revere Water’s shareholders’ equity accounts and total shareholders’ equity on this date. Revere Water’s total liabilities on December 31, 2012, are $7,400. What is Revere Water’s debt ratio on this date? Was there a profit or a loss for the year ended December 31, 2012? How can you tell? At what price per share did Revere Water issue common stock during 2012?

Use the properties of the real numbers to simplify the expression.

x-0.37x

Determine whether the function is increasing, decreasing or neither. $f(x)=-x^{3}-3 x+1$

Replace the underlined word in each sentence below with the appropriate synonym from the following list: validity, evolved, implement, considerably, concept, and controversial. The tax code has changed $\underline{substantially}$ since its origin.

The half-life of $^{238}U$ is $4.5 \times 10^{9}$yr. A sample of rock of mass 1.6 g produces 29 dis/s. Assuming all the radioactivity is due to $^{238}U$, find the percent by mass of $^{238}U$ in the rock.

Using the current year, journalize the following transactions on page 6 of a general journal. Source documents are abbreviated as: credit memorandum, CM; sales invoice, S. Transactions: June 3. Granted credit to Wilbanks and Associates for merchandise returned, $457.00, plus sales tax,$36.56, from S356; total, $493.56. CM41. June 6. Granted credit to Westfall High School for damaged merchandise,$67.00 (no sales tax), from S345. CM42.