Question The projection lens in a certain slide projector is a single thin lens. A slide 24.3 mm high is to be projected so that its image fills a screen 1.83 m high. The slide-to-screen distance is 3.10 m. (a) Determine the focal length of the projection lens. 42.73258 What is the relationship between the slide-to-screen distance and the object and image distances? mm (b) How far from the slide should the lens of the projector be placed to form the image on the screen? 43 3384593x If the object is located at the focal point the image is formed at infinity, mm

4. A giant space station in the shape of a wheel is being evac- uated. The space station is rotating about an axis through its center of mass that is perpendicular to the wheel. Each wave of evacuees consists of one thousand 4.0 X 10'-kg escape pods. The launchers are constructed such that the pods leave the station with a velocity directed straight out- ward from the rotation axis. Model the station before the release of the first wave of evacuees as a cylindrical hoop of radius 1.8 km and mass 1.0 X 108 kg rotating at a rate of 27 rad/min. The rotational inertia of a hoop with mass M and radius R is MR2. a. Explain why the ejection of the pods changes the rota- tional speed of the station but does not change the angular momentum of the station. b. Calculate the change in angular speed of the station after the first wave of evacuees has left the station. Express your answer in rad/s.

3.26. An LTI system has the impulse response h(t) = e ault – 1), where a > 0. = (a) Determine whether this system is causal. (b) Determine whether this system is stable.

Part A - Ideal op amp circuits with a voltage source: part 1 For the circuit shown, determine V. iz. and i, when V= 2 V R = 4 kN Rg = 4 k22 and R3 = 25 kN2 Assume that the op amp is in its linear region of operation Express your answer to two significant figures using appropriate units. View Available Hints) R3 = 25 kg w 1 ix = VCC mA R = 42 w V = 2 v -V R2 = 42 Vo = V 10 = IMA Part B - Ideal op amp circuits with a voltage source: part 2 For the circuit shown (Figure 1), determine the range (ie, maximum and minimum values) of V, so that the op amp operates in the linear region. Assume that R1 = 8 kN. R2 = 8 kN. R3 = 15 k2 and Va = 10 V Express your answer in volts to two significant figures separated by a comma. View Available Hint(s) V Η ΑΣΦ UT vec ? minimum V.. maximum V. = V Submit Part C - Ideal op amp circuits with voltage and current sources Determine V. when V =3V.I, = 1.6 mA R1 = 2 ks2. R2 = 20 kN2, and R3 = 10 k12. Assume that the op amp is in its linear region of operation. (Figure 2) Express your answer to two significant figures and include the appropriate units. | View Available Hint(s) μΑ ? V. = Value Units Submit

P2 Consider the linear system of two ODES dy = Ay, dt where A= : [ -1 -2 2 -1 a Find the eigenvalues of the matrix A. [1 mark] b Calculate the bound h for the stepsize h such that h <h characterizes asymptotic stability of the zero solution when Euler's method is applied to this system. [3 marks]

need help in below tasks COLUMNA COLUMNB 1. ? = A. 4x B. 4* 2. . 3. (合) C. 4 . D. x 1- 4. = E. x2 . 5. F. 2x S(-2) dx = * - 4 In|x[ + C x c )dx = 6Væ+C S (37« + ) dx = 2(x + 3) + C ? dx = In[x] - e* + C ſ 22+3x dx = 4 mo 5(2-1)dx SO(x2 - 2 + ) dx = x(x3 - 4x + 4) + C Scot? x + 2)dx = x ? +C Scsc?x dx cotx S In(1+cos3x) dx +C In 8 32x In x1 +C 2 In 3 3 G. 8* 6. ? H. 2x 7. - = 1. sinºx 8. J. 3 sin x K. sin(3x) L. 32x 9. +C 3 ? 10. +C M. Vx2 1+cos 3x 3 2 11. +C N. xe 3 2(cos x)(sinºx) dx = 5 In (3x) 5in (3x) S +C 12. 0. dx 4 ? P. cotx 13. 3 2 Q. cotx 14. -dx =*+ S(x* – 3x3 + 2-2)dx = *(8x*–30x®+53-80) ? S dx = 4x + c +C R. 2 cotx 40 15.

P2 Consider the linear system of two ODES [ 2 -1 1. dy 1 Ay, where A= dt -2 a Find the eigenvalues of the matrix A. [1 mark] b Calculate the bound h for the stepsize h such that h <h characterizes asymptotic stability of the zero solution when Euler's method is applied to this system. [3 marks]