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Ten Transformation Rules
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Gravity
Terms in this set (11)
(x,y)
preimage
(x+n,y)
horizontal translation
(x,y+m)
vertical translation
(x+n,y+m)
diagonal translation
(-x,y)
horizontal reflection over y axis
(x,-y)
vertical reflection over x axis
(-x,-y)
180 degree rotation clockwise and counterclockwise about the origin
(-y,x)
90 degree rotation counterclockwise around the origin or 270 degree clockwise rotation about the origin
(y,-x)
270 degree rotation counterclockwise about the origin or 90 degree clockwise rotation about the origin
(y,x)
reflection over y=x
(-y,-x)
reflection over y=-x
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Verified questions
ENGINEERING
A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 10 times the instantaneous velocity. Determine whether the mass passes through the equilibrium position if (a) the mass is initially released from rest from a point 1 meter below the equilibrium position, and then (b) the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 12 m/s. In each case find the time at which the mass attains its extreme displacement from the equilibrium position. What is the position of the mass at this instant?
ENGINEERING
A parallel RLC circuit has L = 2 H and C = 0.25 F. The value of R that will produce unity damping factor is: (a) 0.5 Ω (b) 1 Ω (c) 2 Ω (d) 4Ω
ENGINEERING
Two finned surfaces with long fins are identical, except that the convection heat transfer coefficient for the first finned surface is twice that of the second one. What Statement below is accurate for the efficiency and effectiveness of the first finned surface relative to the second one? (a) Higher efficiency and higher effectiveness (b) Higher efficiency but lower effectiveness (c) Lower efficiency but higher effectiveness (d) Lower efficiency and iower effectiveness (e) Equal efficiency and equal effectiveness
ENGINEERING
A hard-drawn spring steel extension spring is to be designed to carry a static load of 18 lbf with an extension of $\frac{1}{2}$ in using a design factor of $n_{y}=1.5$ in bending. Use full-coil end hooks with the fullest bend radius of $r=D / 2 \text { and } r_{2}=2 d$. The free length must be less than 3 in, and the body turns must be fewer than 30. (Note: Integer and half-integer body turns allow end hooks to be placed in the same plane. However, this adds extra cost and is done only when necessary.)
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