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Consider the situation shown in Figure 2.13, which depicts two coordinate systems. The rst coordinate system, denoted by (n, e, d), is the geographic frame. The second coordinate system, denoted by (u, v, w) is the vehicle body frame which is at an arbitrary orientation relative to the geographic frame2 . The relationship between vectors in the body and geographic reference frames can be completely described by the rotation matrix Rg . This rob tation matrix can be de ned by a series of three plane rotations involving the Euler angles3 ( , , ) where represents roll, represents pitch, and represents yaw angle4 . In Figures 2.14 2.16, the axes of the geographic frame are indicated by the I, J, and K unit vectors. The rst rotation, as shown in Figure 2.14, rotates the geographic coordinate system by radians about the geographic frame d-axis (i.e., K unit vector). This rotation aligns the new I -axis with the projection of the vehicle u-axis onto the tangent plane to the ellipsoid. The plane rotation for this operation is described as t x x y = R1 y (2.40) g z z cos( ) sin( ) 0 where R1 = sin( ) cos( ) 0 = [ ]3 . The resultant I and J -axes g 0 0 1 still lie in the north-east tangent plane. The second rotation, as shown in Figure 2.15, rotates the coordinate system that resulted from the previous yaw rotation by radians about the

You also need to import the packages of the Google API that deal with GTalk:

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The distance between them is growing at the rate of 30 40 70 mph. The question then becomes, how long will it take a body moving 70 mph to travel 35 miles Let t represent the number of hours the cars travel after leaving the intersection. 70t 35 35 t 70 1 t 2 In half an hour, the cars will be 35 miles apart. Katy left her house on a bicycle heading north at 8 mph. At the same time, her sister Molly headed south at 12 mph. How long will it take for them to be 24 miles apart The distance between them is increasing at the rate of 8 12 20 mph. The question then becomes How long will it take a body moving 20 mph to travel 24 miles Let t represent the number of hours each girl is traveling. 20t 24 24 t 20 6 t 11 5 5 The girls will be 24 miles apart after 11 hours or 1 hour 12 minutes. 5

train your midsection with weights because it will make your waist bigger. Instead, you should perform endless sets of sit-ups without resistance (and I know of trainees who employ 2,000 repetitions per day in this exercise) to develop your midsection without increasing its size. I ask you: how can you develop any muscle group without increasing its size If this is a legitimate phenomenon, what then could the word develop possibly denote If you train to develop your muscles, then something about their existing condition must change for the better that is, they must get stronger. The stronger a muscle gets, the bigger it gets. This is elementary physiology. Therefore, any attempt to develop a particular

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Once we have the matrix in the unit diagonal form, assuming we haven t made any mistakes, the values x, y, and z represent the solution to the original three-by-three linear system. We can reduce the values we have found, if they are fractions, to their lowest forms. Finally, we should plug our answers into the original equations to be sure we ve arrived at the correct solution to the system.

0.25 -::::(142:9.81 68.1

Finding the absolute minimum or maximum When we know the x-intercepts of a quadratic function with two real zeros, it s easy to find the x-value of the absolute minimum or maximum of its graph. It s the arithmetic mean, or average, of the zeros r and s. If a > 0 in the polynomial, then the parabola opens upward, and we have an absolute minimum somewhere. Let s call its x-value xmin. Then

The Gira e ORDER TABLE for 5 (Key Text Facts About Biological Order Within An Organism)

Several factors are known to increase the liability to stroke, and it has been here that large-scale public health measures have had a

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