. Let T : R n → R m be a linear transformation and A the standard matrix of T. (a) Let BN = {~v1, . . . , ~vr} be a basis for ker(T) (i.e. Null(A)). We extend BN to a basis for R n and denote it by B = {~v1, . . . , ~vr, ~ur+1, . . . , ~un}. Show the set BR = {T( r~u +1), . . . , T( ~un)} is a basis for range(T) (i.e. col(A)). Conclude that dim(col(A)) = n − dim(Null(A)). (b) Show that row(A) = Null(A) ⊥ (i.e. ker(T) ⊥). (c) We have established that for any subspace W of R n (or of any finite dimensional vector space V ), dim(W) + dim(W⊥) = dim(R n ) = n (or dim(W)+dim(W⊥) = dim(V )). Conclude that dim(col(A)) = dim(row(A)).
In: Advanced Math
DATA SHEET
| Titration 1 | Titration 2 | Titration 3 | |
| Mass of KHP, grams | .10 g | .10 g | .10 g |
| Initial volume of NaOH, ml | 0.0 | 6.2 | 12.1 |
| Final volume of NaOH, ml | 6.2 | 12.1 | 17.5 |
CALCULATIONS AND RESULTS
1. number of moles of KHP: n = mass KHP x (1 / 204 g/mol)
n 1 = ______________ n2 =_____________ n3 =___________________
2. number of moles of NaOH = number of moles of KHP
n 1 = __________________ n2 =___________________ n3 =______________________
3. Volume of NaOH used in each titration = final volume of NaOH - initial volume of NaOH
V 1 = _________________ V2 =___________________ V3 =_______________________
4. Molarity of NaOH solution = n/V
M 1 = _________________ M2 =___________________ M3 =______________________
2. Average molarity of NaOH:
M = (M1 + M2 + M3) / 3 = ________________________________________
In: Chemistry
A professor tests whether the loudness of noise during an exam (low, medium, and high) is independent of exam grades (pass, fail). The following table shows the observed frequencies for this test. Noise Level Low Medium High Exam Pass 21 17 8 46 Fail 8 6 10 24 29 23 18 N = 70 (a) Conduct a chi-square test for independence at a 0.05 level of significance. (Round your answer to two decimal places.) $ \chi_{obt}^2 $ = Decide whether to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis. Correct: Your answer is correct. (b) Compute effect size using Cramer's V. (Round your answer to two decimal places.) V =
In: Statistics and Probability
Problem 3: A capacitor of capacitance C = 2 μF has been charged so that the potential difference between its plates is V0 = 85 V. The capacitor is then connected to a resistor of resistance R = 5.5 kΩ. The switch S is closed, and the capacitor begins to discharge. C = 2 μF V0 = 85 V R = 5.5 kΩ Calculate the time constant τ of the circuit in seconds. Calculate the charge Q0 on the capacitor before the switch is closed, in coulombs. Calculate the current I0 immediately after the switch is closed, in amperes. Calculate the potential difference VC in volts between the capacitor plates at time t = 5.0 ms after the switch is closed. Calculate the time T in s after which the charge on the capacitor has decreased to one fourth its maximum value.
In: Physics
Lionel, a single taxpayer, reported $46,175 of
self-employment income on his 2018 Schedule SE, Section B, Line
6.
Lionel also received two Forms W-2 in 2018; the
applicable amounts for Medicare wages and Medicare tax withheld are
summarized below:
Lionel's W-2 Forms
Form W-2 DescriptionForm W-2 Box
#AmountEmployer A
Medicare wages and tipsBox 5119,000.00Employer A
Medicare tax withheldBox 61,725.50Employer B
Medicare wages and tipsBox 570,000.00Employer B
Medicare tax withheldBox 61,015.00
Directions
Prepare Form 8959 (Parts I, II, IV, V)
Download Form 8959 - Compensation Practical
Application.pdf.
Complete Parts I, II, IV and V of Form 8959 using the
case information provided above.
Submit the completed tax form
In: Accounting
A substance whose state is pecified by P,V,T can exist in two distinct phases. At a given temp T the two phases can coexist if the pressure is P(T).
The following information is known about the two phases. At the temps and pressures where they can coexist in equilibrium,
i) There is no difference in the specific volume of the two phases
ii) there is no difference in the specific entropy of the two phases
iii) the specific heat cp and the volume expansion coefficient a(alpha) are diffrent for the two phases
a) Find dP(T)/dT as a fuction of T.
b) What is the qualitative shape of the transition region in the P-V diagram? In what way is it different from that of an ordinary gas-liquid transition? ( The phase transition we have described is a second-order transition.)
In: Physics
Consider a process in which one mole of
a monatomic ideal gas is compressed from
a volume of V1 =1.459m3 to V2 =1m3 at a
constant temperature of T =353.7 K.
(a) What is the entropy change of the gas (in
J/K units)?
(b) What is the change in the value of PV for
the gas (in J units)?
(c) What is the energy change of the gas (in J
units)?
(d) What is the enthalpy change of the gas
(in J units)?
(e) What is the Helmholtz energy change of the
gas (in J units)?
(f) What is the Gibbs energy change of the gas
(in J units)?
23. Perform a Legendre transform of U(S, V,Ni) in
order to obtain a new potential function whose
natural variables are S, P, and Ni (and make
sure to indicate the partial derivative that is
used in order to transform the variable V to P
In: Chemistry
|
A voltaic cell is constructed from |
Part A By using data in Table 20.1 in the textbook, calculate the standard emf of this voltaic cell.
|
| E∘ = |
| V |
SubmitMy AnswersGive Up
Part B
Will the concentration of Ni2+(aq) increase or decrease as the cell operates?
Will the concentration of increase or decrease as the cell operates?
| will increase |
| will decrease |
SubmitMy AnswersGive Up
Part C
What is the initial concentration of Ag+(aq) in the Ag+−Ag half-cell?
Express your answer using one significant figure.
|
|
| [Ag+(aq)]i = |
M
In: Chemistry
Hydrogen, acting as a van der Waals gas (EOS shown below), is compressed in an isothermal closed system process from 6.236m3/kg to 0.629m3/kg at 300K. What is the change in specific entropy of the gas? (use the entropy change relation in chapter 12)
P = RT/( v − b) − a/( v^2) (1)
a = 27R^2Tcrit^2/(64Pcrit) (2)
b = RTcrit/ (8Pcrit) (3)
Following example 12-7 in the book the change in internal energy of a van der Waals gas for an isothermal process can be derived (the result is shown below). Using the definition of boundary work (wb = R P dv) and conservation of energy what is the amount of heat which is rejected by the compression process?
u2 − u1 = a (1/v1 − 1/v2)
In: Mechanical Engineering
Which of the following is/are applicable to a contract which is
deemed ‘void’ in a contractual
dispute?
(i) The injured party can choose to repudiate the contract.
(ii) The law would regard the contract as never having
existed.
(iii) Where goods have transferred from party A to party B under
the contract, B may retain
ownership of the goods.
(iv) Where goods have transferred from party A to party B under the
contract, B must return
the goods to A.
(v) Where goods have transferred from party A to party B under the
contract, and party B
has then transferred the goods to party C, C may retain ownership
of the goods.
a. (i) and (iii) only.
b. (ii) and (iv) only.
c. (i), (iii) and (v) only.
d. All of the above.
In: Operations Management