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5. Suppose that matrix A can be transformed into matrix B by elementary row operations: $$A = \begin{bmatrix} -2 & -5 & 8 & 0 & -17 \\ 1 & 3 & -5 & 1 & 5 \\ 3 & 11 & -19 & 7 & 1 \\ 1 & 7 & -13 & 5 & -3 \end{bmatrix} \rightarrow B = \begin{bmatrix} 1 & 0 & 1 & 0 & 1 \\ 0 & 1 & -2 & 0 & 3 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix}$$ a. Find a basis for the row space of A. b. Find a basis for the column space of A. c. Find the nullspace of A. d. Find rank(A). e. Find nullity(A). f. Find rank($$AA^T$$). g. Find nullity($$AA^T$$). h. Let T(x) = Ax where x is a vector. What is the domain of T? i. What is the codomain of T? j. Is T an onto function? Explain your answer. k. Is T a one-to-one function? Explain your answer.

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Draw out a “unicorn” 13C-NMR spectrum. a. Indicate all potential peaks for each region. b. Make sure all signals are in the proper region with appropriate ppm values. c. Label what bonding neighborhood is represented. (i.e., sp3C connected to a sp3C, vinylic C in C=C bond, and so on)

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Problem No 6: Liquid (temperature t=0 °C) flows from the lower reservoir to the upper reservoir through the serially connected pipeline. The lower reservoir is under the gage pressure pm, while the upper reservoir is under the vacuum pressure pv. The diameters of the pipes are d and D, lengths are 1 and L. Calculate difference of elevations in the reservoirs h if surface roughness $\Delta_s$ =0.1 mm. The coefficients of minor losses for entrance are $K_m$ =0.5, for exit $K_m$ =1.0. Use Borda-Karnot relation for sudden expansion $K_m$ = (1-$A_1$/$A_2$). Liquid: ethylene glycol 80% D, mm 55 d, mm 35 L, m 18 l, m 16 pmn, kPa 250 Pvk, kPa 17 Q, l/s 5 Pmn 又 4 d,l D,L Q Fig.6 Pvk 又

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Microorganisms whose optimal growth temperature is 37°C (normal human body temperature) are classified as Multiple Choice thermophiles. psychrophiles. mesophiles. extreme thermophiles.

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We have three resistances each of 1 ohm. How many different values of resistance can be obtained by different series-parallel combinations if all the three resistances are to remain in the circuit? a. three b. four (correct) c. five d. six

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Question 13 (1 point) The pH of a solution of 0.15 mol/L methanoic acid is a.bc • record your answer in the blank • do not include units Your Answer:

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What is the formal charge on phosphorus in the following Lewis structure of PO$_4$$^{-3}$? [ :O:: \ \ O-P-O: \ \ :O:: ]$^{-3}$ O -2 O -1 O 0 O +1 O +2

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What occurs in a labor market when a shortage of labor arises? 3 tries left The ____ to eliminate the shortage. A. real wage rate rises B. real wage rate falls C. demand for labor decreases D. supply of labor increases

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You conduct genomic analysis on two patients, patient A and patient B, who have both developed a resistance to crizotinib, to identify new mutations that could play a role in this resistance. You find that patient A has developed an EGFR c.2573T>G (L858R) mutation, an activating mutation in another receptor tyrosine kinase that activates many of the same signaling pathways as ALK. Patient B has developed a secondary mutation in the kinase domain of ALK, ALK c.3586C>A (L1196M). Crizotinib is more likely to still be inhibiting ALK in patient ____________. Ceritinib, a second generation ALK inhibitor that binds more tightly to the kinase domain would be more likely to overcome this resistance in patient ____________. A; A A; B B; A B; B

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Jones and Funk Corporation is authorized to issue 6,000,000 common shares. During 2024, Jones and Funk had the following share transactions: Jan. 1 Issued an initial 550,000 shares at $6 per share. June 30 Declared a $0.10 per share dividend to shareholders of record payable August 1. Dec. 27 The board of directors declared a 10% common stock dividend. The market price of the common shares on this date was $7.50 per share. Instructions Record the above transactions for Jones and Funk Corporation. Use correct journal format.

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nicholas s.