LINEAR ALGEBRA
If A = Aᵀ and B = Bᵀ, which of these matrices are certainly symmetric? (a) A² - B² (b) (A + B)(A - B) (c) ABA (d) ABAB.
LINEAR ALGEBRA
For two invertible $n \times n$ matrices $A$ and $B$, determine the formulas stated below is necessarily true. $$ ABA^{-1} = B $$
DISCRETE MATH
Draw the transition diagram of a finite-state automaton that accepts the given set of strings over {a, b}. Ends with aba
LINEAR ALGEBRA
Let A and B be symmetric n × n matrices. For the following, determine whether the given matrix must be symmetric or could be nonsymmetric: F = ABA
GEOGRAPHY
Which of the terms above can also be applied to the United States? Explain.
ACCOUNTING
On October 4 the owner of Wilder ness Rentals deposited the following in the business checking account at First National Bank. The beginning balance in the account is $3,306.54 before these transactions. Cash: Currency,$374.00; Coins, $7.42 Checks: Bob Warner, drawn on Consumers Bank, ABA No. 63-706;$64.98 Joan Walkman, drawn on Mountain Bank, ABA No. 63-699; $349.81 Ernesto Garcia, drawn on Progressive Savings and Loan, ABA No. 63-710;$29.44. In your working papers: 1. Place a restrictive endorsement on each check. Use “Wilderness Rentals.” 2. Fill out a deposit slip. Use the ABA number to identify each check. 3. Record the deposit in the checkbook on Check Stub 651.
LINEAR ALGEBRA
For two invertible $n \times n$ matrices $A$ and $B$, determine the formulas stated below is necessarily true. $$ (ABA^{-1})^3 = AB^3A^{-1} $$
LINEAR ALGEBRA
Let A and B be Hermitian matrices. Answer true or false for the statement that follows. Explain or prove your answer. The eigenvalues of ABA are all real.
ENGINEERING
Showing all intermediate results, calculate the following expressions or give reasons why they are undefined: b^TAb, aBa^T, aCC^T, C^Tba
PHYSICS
When a certain force is applied to an ideal spring, the spring stretches a distance x from its unstretched length and does work W. If instead twice the force is applied, what distance (in terms of x) does the spring stretch from its unstretched length, and how much work (in terms of W) is required to stretch it this distance?
ALGEBRA
Examine the following sequence. $$ 1,1,2,3,5,8,13,21, \ldots $$ Identify the rule being applied to the pattern, and find the next three terms.
ALGEBRA
Each letter represents a single digit from 0 to 9. Find all possible values of each digit that make the arithmetic exercise true. $$ ABA+BAB=CCC $$
COMPUTER SCIENCE
Answer each part for the following context-free grammar G. $$ \begin{array}{l}{R \rightarrow X R X | S} \\ {S \rightarrow \mathrm{a} T \mathrm{b} | \mathrm{b} T \mathrm{a}} \\ {T \rightarrow X T X|X| \varepsilon} \\ {X \rightarrow \mathrm{a} | \mathrm{b}}\end{array} $$ a. What are the variables of G? b. What are the terminals of G? c. Which is the start variable of G? d. Give three strings in L(G). e. Give three strings not in L(G). f. True or False: $T \Rightarrow \mathrm{aba}$. g. True or False: $T \stackrel{*}{\Rightarrow} \text { aba. }$. h. True or False: $T \Rightarrow T$. i. True or False: $T \stackrel{*}{\Rightarrow} T$. j. True or False: $X X X \stackrel{*}{\Rightarrow} \text { aba. }$. k. True or False: $X \stackrel{*}{\Rightarrow} \text { aba }$. l. True or False: $T \stackrel{*}{\Rightarrow} X X$. m. True or False: $T \stackrel{*}{\Rightarrow} X X X$. n. True or False: $S \stackrel{*}{\Rightarrow} \varepsilon$. o. Give a description in English of L(G).
CALCULUS
Suppose that A is an invertible $n \times n$ matrix. (a) Prove that $P^n$ is invertible, for any positive integer n. (b) Prove that if B and C are $n \times n$ matrices such that ABA=ACA, then B=C. (c) If $A^{2}=A$ (we say that A is idempotent), find A.
CHEMISTRY
a. What do the terms saturated and unsaturated mean when applied to hydrocarbons? b. What other meanings do these terms have in chemistry? c. Classify alkenes, alkanes, alkynes, and aromatic hydrocarbons as either saturated or unsaturated.
ENGINEERING
Determine the moment M applied to the lower link through its shaft which is necessary to support the load P in terms of the angle $\theta$. Neglect the weights of the parts.
ENGINEERING
A horizontal force P is applied to the four-bar mechanism shown. If the weight of the bars is negligible compared with the applied force P, determine the magnitude of the couple M needed to hold the mechanism in equilibrium at the orientation shown. (Note: For simplicity, leave your answer in terms of $\theta, \phi, \text { and } \psi$.)
PHYSICS
Starting at time t=0, net force $F_{1}$ is applied to an object that is initially at rest. (a) If the force remains constant with magnitude $F_{1}$ while the object moves a distance d, the final speed of the object is $v_{1}$. What is the final speed $v_{2}$ (In terms of $v_{1}$) if the net force is $F_{2}=2 F_{1}$ and the object moves the same distance d while the force is being applied? (b) If the force $F_{1}$ remains constant while it is applied for a time T, the final speed of the object is $v_{1}$. What is the final speed $v_{2}$ (in terms of $v_{1}$) if the applied force is $F_{2}=2 F_{1}$ and is constant while it is applied for the same time T?
ALGEBRA
Examine the following sequence 1, 1, 2, 3, 5, 8, 13, 21, .... Identify the rule being applied to the pattern, and find the next three terms.
ENGINEERING
Let $\varphi$ be a scalar field and F a vector field. Derive expressions for $\nabla \cdot(\varphi \mathbf{F})$ and $\nabla \times(\varphi \mathbf{F})$ in terms of operations applied to $\varphi(x, y, z)$ and to $\mathbf{F}(x, y, z)$.
COMPUTER SCIENCE
A set S of strings of characters is defined recursively by 1. a and b belong to S. 2. If x belongs to S, so does xb. Which of the following strings belong to S? a. a b. ab c. aba d. aaab e. bbbbb
LINEAR ALGEBRA
$$ \begin{equation*}A=\begin{bmatrix}2&&1\\4&&-1\end{bmatrix}, B=\begin{bmatrix}2&&3\\4&&6\end{bmatrix}\end{equation*} $$ Compute ABA, or give the reason why the expression is not defined.
QUESTION
Nish has received a new bike for his sixth birthday. Explain how each of the following terms can be applied as he learns to ride the bike. • Shaping • Reinforcement • Generalization
QUESTION
The SWR Group advertised for applicants for secretarial, clerical, and typist positions. Respondents could apply for one or more of the positions. The responses were as follows: 12 applied for secretary. 10 applied for clerk. 14 applied for typist. 7 applied for secretary and typist. 5 applied for secretary and clerk. 3 applied for clerk and typist. 2 applied for all three. 3 applied for none of the positions. Draw a Venn diagram and use it to find the following. (a) What was the total number of respondents? (b) How many applied for the typist position only? (c) How many applied for the secretary position but not the clerk position?
ACCOUNTING
On August 14 Loretta Harper, owner of Peabody Cards and Gifts, deposited the following items in the checking account of the business. Cash: $784.29 Checks: Charles Ling, drawn on American Bank of Commerce, ABA No. 32-7091;$39.44 Keith Lopez, drawn on People’s Bank, ABA No. 84-268; $22.95 Marjorie Luke, drawn on Horizon Federal Savings and Loan, ABA No. 84-6249;$52.95 Mable Parker, drawn on Security National Bank, ABA No. 84-2242; $67.45 On August 15 Peabody received the July bill from Northeast Telephone for$214.80. On August 17 Peabody received an advertising bill from the Bayside News for $275.00. Using the forms provided in your working papers: 1. Complete a deposit slip. 2. Record the deposit on the check stub for Check 41. 3. Record the information for paying the telephone bill on Check Stub 41 and complete the check stub. Use August 16 as the date. 4. Prepare Check 41 to pay the telephone bill and sign your name as drawer. 5. Prepare the check stub and Check 42 to pay the bill for advertising. Use August 17 as the date and sign your name as drawer.