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Draw the nucleotide base pairing of A-U (10 Points) (Be cognizant of space)
Let V be a finite dimensional vector space over R with an inner product 〈x, y〉 ∈ R for x, y ∈ V . (a) (3points) Let λ∈R with λ>0. Show that 〈x,y〉′ = λ〈x,y〉, for x,y ∈ V, (b) (2 points) Let T : V → V be a linear operator, such that 〈T(x),T(y)〉 = 〈x,y〉, for all x,y ∈ V. Show that T is one-to-one. (c) (2 points) Recall that the norm of a vector x ∈ V...
Original DNA sequence (coding strand), starting at the beginning of the gener Normal: 5-ATGATCTCCTAATACAA... Mutation: 5'-TTGATCTCCTAATACAA... 30. Can a single nucleotide be a conserved sequence? Explain your answer. (4 points) 31. Explain why self-splicing introns support the RNA world first Hypothesis (life evolved via RNA). (3 Points) 32. How can the speed of DNA replication increase, while the rate of replication remains constant7 For example, if each chromosome in the human genome initiates DNA replication, at a rate of 50...
7. V={[)a620) a vector space! Draw the vector space? Draw the graph and explain why or why not? I. Verify the axiom for polynomial. p(x) = 2t' +31° +1+1 9(x) = 4r +57 +31 + 2 8. p(t)+9(1) € P. 9. p(t)+q(t) = f(t)+p(1) 10. cp(1) EP A subspace of a vector V is a subset H that satisfies what three conditions? 12. Is 0 a subspace of R" 13. Let V, V, E V; show H = span{v. v)...
Question 5 of 33 Suppose that, at : = 5.00 x 10-s, the space coordinates of a particle are x = 225 m, y = 30.0 m, and z = 35.0 m according to coordinate system S. If reference frame S' moves at speed 1.42 x 10 m/s in the +x-direction relative to frame S. compute the corresponding coordinate values as measured in frame S'. The reference frames start together, with their origins coincident at I = 0. כח m...
2. Let V be the vector space of polynomials in two variables r and y of degree at most two: V-(ar' + bry + суг + dr + ey + f | a,b,c, d, e, f E R} Let T be the linear operator on V defined by Find the Jordan canonical form of T
2. Let V be the vector space of polynomials in two variables r and y of degree at most two: V-(ar' + bry + суг...
Q2 (10 points) Let V- Ps be the vector space of polynomials of degree 3. Let C (1,x 2, 2)2 +2)3) be two ordered bases of V. () Find the change-of-basis matrices Pc-B and PB-c (ii) Find [y]в if [v]c- (1, 0, 0, 1). (iii) Find [y]c if [y]B-( 1, 0, 0, 1).
3. (10 points) in free space, E = 20xa, + 40yay-Oza, V/m. Calculate the work done in transferring a 2 mC charge along the arc r= 2,0 < φ < π/2 in the z = 0 plane.
Q4 6 Points Let V be a vector space over R and let V1, ... , Vn each be a vector in V \{0}. Show that (v1, ..., Vn) is linear independent if and only if span(v1, ... , Vi) n span(vi+1, ..., Vn) = {0} for all i = 1,...,n - 1