LINEAR ALGEBRA Prove or disapprove (no counterexamples):

Given that sets A = {u₁....u_n} and B = {v₁....v_n} are subsets vectors of a vector space V.

If the vectors in A and B, respectively, are independent and dim(Span(u₁....u_n)) = dim(Span(v₁....v_n))

then Span(u₁....u_n) = Span(v₁....v_n)

Estimate the heat of vaporization of diethyl ether at its normal boiling point using Trouton’s rule and Chen’s rule and compare the results with a tabulated value of this quantity. Calculate the percentage error that results from using each estimation. Then estimate ΔH^v at 100°C using Watson’s correlation.

Compare the measured values of tension to the calculated values of tension. What are the possible physical experiment uncertainties for the differences between the measured and calculated?

Measured= .075N

Caculated= .079N

Velocity v = .433m/s

Mass of Cylinder m = .1118kg

Radius of Pendulum r = .265

T=mv2/r

Four resistors are connected to a battery as shown in the figure. The current in the battery is I, the battery emf is ? = 6.20 V, and the resistor values are R1 = R, R2 = 2R, R3 = 4R, R4 = 3R. Find the voltages across each resistor. R 1, R2 and R3 are in series. R4 is in parallel.

Explain how case law Right of Ontario v Ron Engineering & Construction (Eastern) Ltd. [1981] S.C.R. 111 played a pivotal role in establishing new contract concepts in Canada?

-  details and key facts of the claim

- contribution of the court’s decision to establish new bidding rules and laws

When a 23.0-V emf device is placed across two resistors in series, a current of 14.0 A is flowing in each of the resistors. When the same emf device is placed across the same two resistors in parallel, the current through the emf device is 64.0 A. What is the magnitude of the larger of the two resistances?

When a 26.0-V emf device is placed across two resistors in series, a current of 11.0 A is flowing in each of the resistors. When the same emf device is placed across the same two resistors in parallel, the current through the emf device is 59.0 A. What is the magnitude of the larger of the two resistances?

iv) How can the true color of objects be affected by artificial lighting? Explain briefly.

v) “The room is too loud. My ears are ringing everyday” What type of room is this? Suggest solution / solutions for this problem.

vi) What does it mean that a room has good sound control ?

At what pH is the cell potential of the following half-cell +1.20 V?
Cr2O₇ ^2- (aq) + 14H⁺ (aq) + 6e^- → 2Cr₃ + (aq) + 7H₂O (l)
The temperature is 298 K, the pressure is 1 bar and the concentration of Cr2O₇ ^2- (aq) and Cr₃⁺ (aq) is 1 mole dm^-3

Two 0.25 cm radius coins are separated by a 0.1 mm thick piece of paper with dielectric constant kappa = 6.475. They form a capacitor. A 8 V battery is connected to the capacitor. How much charge is stored on each coin? The area of a circle is given by pi r^2. C