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A. Consider complex plane C and identify it with a plane R2 in 3D-space Rº with basis vectors i, j, k, so the real line goes along i and imaginary line along j. Then a complex number z = x + yi is identified with a vector z = xi+ yj. Show that the inner (dot) product and vector product of z and w are given by z. = Re(zw), Ž x ū = Im(zw)k.
The incident TEM Plane Waves with medium 1 are: Hiz (X) = AT EGB2) eUwt) %3D Ery (X) = A Ty eUB1x)eJwt) 0, E, U E, , Ho 1 W. In the medium 2 the conductivity is not metallic and satisfies the relationship: Determine the vectors E and H reflexed in medium 1. Write your answer clear.
Question 5. [5pt total] Consider a cuboid in 3D-space that is resting on the ty-plane, with one vertex at the origin, and the vertex farthest from that vertex is at (4,5,3). What are the coordinates of the other 6 vertices? 4 3 (4,5,3) 2 6 1 -2 3 2 -1 2 3 -2 Coordinates:
4. (4.5 pts) Consider a 3D electromagnetic plane wave in vacuum, described in usual complex form by, (r, t) = Ēelkr-wt) in which ło = Epein/2y. Where k = -kx is the wave vector (assume k > 0) and w > 0 is the angular frequency. As usual, the real field is Er, t) = ReLEr, t)] (a) In which direction is the wave propagating? In terms of the given values k and w, what is the speed, wavelength, and...
Two stars with masses 2.75 x 1030 kg and 5.92 x 1030 kg form a binary system. If the two stars have an average separation of 5.96
The two stars in a binary star system have masses 2.2×1030 kg and 5.8×1030 kg . They are separated by 2.3×1012 m . What is the system's rotation period, in years? What is the speed of the lightest star? What is the speed of the heaviest star?
Line segment AB is shown in the coordinate plane below. A math teacher states the dilation of a line segment is longer or shorter in the ratio given by the scale factor. please based on picture . identify a scale factor for a dilation through the origin so that the dilation is longer than AB. Draw the dilation on thd coordinate planet , label it CD,and show that CD is longer than AB in the ratio given by the scale...
BIOL 1030 Lab 7 Page 16 Name Student Number BIOL 1030 Lab 7 Assignment - Tear out this page and hand it into your TA. Each Assignment is worth 1% of your final grade. BIOL 1030 Lab Assignments MUST be submitted to your TA before you leave the lab. Question 1 - (10 marks) Label the two diagrams below exine () intine () generative cell (g.c.)[1N) () g.c. plasma membrane () g.c. nucleolus ) g.c. nucleus () tube nucleus [1N]...
Symbolic Physics/Math Equation I. A 30 kg block remains at rest on the 20° inclined plane shown. The block and the plane have friction coefficients ustatic = 0.80 and uinetic= 0.70. Determine the type and amount of friction that acts on the box. (7 points) 200