QUESTION 1 Quadratic Equation Choose one . 5 points 1. Solve I' + 4x-5=0 using the quadratic formula O II = 1, 12 = -5 O II = 1, 12 =5 O = =-1, 12 =-5 QUESTION 2 Global Rotation Choose one . 5 points Write the global rotation matrix of 60" about the world z - aris, "R.(60) O O O QUESTION 3 Global Rotation Choose one . 5 points Write the global rotation matrix of 45" about the world y-axis, CR,(45) O O OGROUP 10 Sphere Equation Group . 4 questions A sphere is the set of points p = (I, y, z)in 30 space that have a constant distance called the radius R with a fixed point c = (a, b, c) defined as the sphere center. The sphere algebraic equation is : (z - a) + (y - b)] + (z- c]] =R where a, b, c are the components of the center QUESTION 10.1 Finding a Sphere Center and Radius Choose one . 5 points Find the center & and radius r of the sphere S: (x + 7)? + (y-4)? + (2+ 9)3 =36 O 2 = (7, -4,9), =6 O 2= (-7,4, -9), T=6 O 2= (7, -4,9), r =36 QUESTION 10.2 Finding a Sphere Center and Radius Choose one . 5 points Find the center & and radius r of the sphere S: (x + 1) + (y-2)) + (z-2)3 =4 O 2= (-1,2, 2), r=2 O 2 = (-1,2, 2), r=4 O 2= (1, -2, -2), r=2 QUESTION 103 Writing the Equation of a Sphere Given its Center and Radius Choose one . 5 points Write the equation of a sphere with center @ = (2, 1, -5) and radius R=3 O (z - 2)3 + (1 - 1)3 + (2+5)? =9 O (1 -2)3 + (y-1) + (2+5)? =3 O (z + 2)2 + (1 + 1)? + (2-5)2=9 QUESTION 10.4 Writing the Equation of a Sphere Given its Center and Radius Choose one . 5 points Write the equation of a sphere with center d = (3, 2, 1) and radius R= 5 O (z -3)2 + (y-2)3 + (2-1)3 =25 O (z -3)3 + (y -2) + (2-1)? =5 O (z +3)? + (y + 2)3 + (2+1)? =5GROUP 11 Colliding Contact, Separation Contact, and Resting Contact Group . 3 questions QUESTION 11.1 Checking contact state. Choose one . 5 points what is the collision state of a body moving with velocity u = (2, -3, 1)m/s with respect to a plane with normal vector fi = (0, 1, 0) assuming the body is above the plane. O Colliding contact O Separation contact O Resting contact O None of the above QUESTION 11.2 Checking contact state. Choose one . 5 points what is the collision state of a body moving with velocity = (1, 2, 4)m/s with respect to a plane with normal vector fi = (1, 1, 0) assuming the body is above the plane. O Colliding contact O Separation contact O Resting contact O None of the above QUESTION 11.3 Checking contact state. Choose one . 5 points what is the collision state of a body moving with velocity = (3, 1, -3)ma with respect to a plane with normal vector fi = (2,3,3) assuming the body is above the plane. O Colliding contact O Separation contact O Resting contact O None of the aboveGROUP 12 Sphere-Sphere Collision Group . 4 questions Given the two spheres : 51 : (x -1)2 + (y - 2) + (z-3)2 =9 and $2 : (x -5)3 + (y-5)3 + (2-3)3 =4 Answer the 4 questions below QUESTION 12.1 Find First Sphere center and radius Choose one . 5 points Find the center ci and radius Ri of sphere 51 O ci = (1,2,3) , RI = 3 O 2 = (-1, -2, -3) , R1 =3 O at = (-1, -2,3) , Ri = 9 QUESTION 12.2 Finding Second Sphere center and Radius Choose one . 5 points Find the center c and radius Ra of sphere 52 O 2 = (-5, -5, -3) , R, =4 O C = (-5,5, -3) , Ra = 2 O 0 = (5,5,3) , Ra = 2 QUESTION 123 Find the Distance between the two Spheres Choose one . 5 points Calculate the distance cica between the two sphere positions O CIC=25 O ac =5 O 90 =1 QUESTION 12.4 Collision between two Sphers Choose one . 5 points Is there any collision between the 2 spheres ? O collision, ge R + R2 O No collision, cc > Ri + Ry O None of the aboveQUESTION 4 Local Rotation Choose one . 5 points Write the local rotation matrix of 30 about the local Y-axis. "Ry(30) O O O N- 9 QUESTION S Local Rotation Choose one . 5 points Write the local rotation matrix of 90 about the local Z-axis, "Rz (90) O 1 0 0 O O QUESTION 6 Transforming a Vector from Local Space to World Space Choose one . 5 points A vector coordinate in body frame coordinate (rigid body) is ro = (4, 5, 3), calculate the vector coordinate in world space ? if the orientation of the rigid body is 90 about the local X-axis. Note :7 = R. To O OQUESTION 7 Transforming a Vector from World Space to Local Space Choose one . 5 points A vector coordinate in world space is F = (1, 0,2), calculate the vector coordinate in body frame coordinate (rigid body) To if the orientation of the rigid body is 90 about the global z-axis. Note: use To = R - F O O O QUESTION B Transforming a Point from Local Space to World Space Choose one . 5 points A box is located at d = (2, 1, 0) with orientation of 90 degree about the global x-axis. Calculate the position Pawl of a point in world space if the point coordinate in local space is Plocal"(4,0,2]- Note : use Punch = C+ R. _ O O O NOA QUESTION 9 Transforming a Point from World Space to Local Space . Choose one . 5 points A box is located at 2 = (1, 1, 0) with orientation of 90 degree about the global z-axis. Calculate the position Plot of a point in in local space if the point coordinate in world space is Poorly = (3, 4, 6) Note: Use Plant = R - (Pru - 2) O -3 O Ch O