-1 1 1 1. Let A = (2 1) ,με R. 4 1 a) (4 marks) For each μ ER find Cartesian equations for Col(A) and Null(A). b) (2 marks) Are the columns of A linearly independent? Give full reasons for your answer (discussion in terms of μER, based on the definition of linear independence).

QUESTION 3: For the beam given in the figure, using the Virtual Work Principle, a) Calculate the slope at B b) Calculate the vertical displacement at B Take E 200 GPa and I=250×106 mmª. Note: P is given for each student in the attached table. A EI 4 m P + ΕΙ 2 m B

c) A thin elastic wire has its both ends tied to two fixed holders and is completely immersed in a flowing fluid. A study is to be carried out to determine the static deflection, 8, at the axis of the wire due to drag that exerted by the flowing fluid. Assume: 8 =f(1, d, p, µ, V, E) where dis a deflection in unit length, I is wire length, d is wire diameter, pis fluid density, u is fluid dynamic viscosity, V is fluid velocity, and E is elastic modulus of the wire. By using Buckingham Pi (t) theorem and basic dimensions system of MLT, predict a suitable set of a Pi (t) terms to study this problem. Use d, p, and V as the repeating variables. The unit of elastic modulus is given as Newton/m?.

Task 4 Find a formula for cos (30) in terms of cos (0) and sin (0) using de Moivre's Theorem.

A massless beam supports two weights as shown. Find W such that the supporting force at A is zero. L- L 4 4 2 826 N A B W Your answer

**DFQ** If you know statics, it helps in understanding. A uniform beam (Constant EI) with Length = L has both ends fixed. Applied loading is a uniformly varying load, zero at the left end, W at the right end. Units of the load are pounds per foot. Your results will be stated in terms of W, L, EI.You will use Laplace Transforms to solve for the beam deflection expression.  Other quantities to be determined from the deflections will use derivatives. Your results will be stated in terms of W, L, EI. (Triangular shaped distributed load) A uniform beam (Constant EI) with Length = L has both ends fixed. Applied loading is a uniformly varying load, zero at the left end, W at the right end. Units of the load are pounds per foot. A) Find the expression for deflection at any point, with x measured from the left end.

Q4. Express the group of variables length (L), kinematic viscosity (v) and velocity (V) as a dimensionless ratio. In other words, find out the dimensionless (pi) π term. Use Buckingham Pi Theorem Hep 1: variables m=3 Aep2. Choose a dimensional system MLT L=ALY V=CLT-¹) V=L²T-1

how to solve this one?