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1. Is T a linear transformation? Justify completely a. T:R → RP defined by T(1, y, z) = (y, 1-22, y) b. T:R + P, defined by T(a,b,c) = (a - cr? - bx +1
and 02 Let T : R2 + RP be the linear transformation satisfying 9 5 Tū1) = [ and T(v2) = [ - -5 -1 X Find the image of an arbitrary vector [ Y -([:) - 1
Show that for any given temperature ratio, t, the optimum pressure ratio, rp,op for which specific work output is maximum, Wmax, is given by the following equation;
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#20, please! Solve equation for variables in this case R1= Rp v_Dm13.k-T Vrms =271 19. . =2π rms ← 2 2 (R + R2)
5. Let T: P2(R) + RP be the linear transformation that has the matrix …_…………..ນະ 1 2 -1 11 1 1 relative to the bases a = 1+ 21,1+1+12,1+for P2 (R) and B = (1,1),(1,-1) for R2. Find the matrix of T relative to the bases d' = 2+3.r,1+1+12,2+3.+r2 for P2(R) and B' =(3,-1),(1,-1) for R2.
3. The following information is provided for oxalic acid: H1ャNatCA H2C2Oa + H2O <-> H30' +HC204" Kal= 5.4 x 10" d) Sketch the shape of the pH titration curve of the 0.200 M Na,C20, with 0.200 M HCI. i) Label the pH of the solution at the beginning of the pH titration ii) Label the pH of the solution at the first and second equivalence. il) Label the pKbı and pKaz on the curve.
QUESTION 2 Rp 80ooker 5pts If R, = 8k12, select the value of Rp accordingly such that v. = 8000(in - ia) v 15 V (1) § 2 ka 6-15 V 1) SRI la=ib
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