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Page "Specular reflection" ¶ 14
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Given and incident
# Given any two distinct points, there is exactly one line incident with both of them.
# Given any two distinct lines, there is exactly one point incident with both of them.
Given that the angle of incidence is larger than the critical angle ( with respect to the normal of the surface ) and the refractive index is lower on the other side of the boundary relative to the incident ray, TIR will occur and no light will be able to pass through.
Given the geometry of the array, the delays or phase differences can be used to estimate the incident angle.
Given Heinlein's carefully cultivated public persona as a curmudgeon, it is amusing that much of the humor in the book consists of riffs on the idea that Ginny is the hothead, while Robert is the easygoing one, e. g., in a shipboard incident at the captain's table, Robert continues eating his dessert after being doused in salad during a food fight started by Ginny.

Given and direction
: Given a point ( in terms of its coordinates ) and the direction ( azimuth ) and distance from that point to a second point, determine ( the coordinates of ) that second point.
Given the differences of opinion within the Lord Aberdeen cabinet over the direction of foreign policy with regard to relations between Britain and the French under Napoleon III, it is not surprising that debate raged within the government as Louis Bonaparte, now assuming the title of Emperor Napoleon III of France.
Given their original purpose, military marching bands typically march in a forward direction with ( no variation of ) straight lines.
Given that this is a plane wave, each vector represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the axis.
Given an embedding of a rooted tree in the plane, if one fixes a direction of children ( starting from root, then first child, second child, etc.
About the new markets, Ergen said, " Given the assets we've been accumulating, I don't think it's hard to see we're moving in a different direction from simply pay-TV, which is a market that's becoming increasingly saturated.
Given the similarities with readings from people living on loess soils, the general direction of the local movement according to Price et al., is from the northeast to the southwest.
Given the direction of the current, it is clear that the buoys would be dragged in the opposite direction to that claimed by Mr Jim Brooks.
Given estimates of the image gradients, a search is then carried out to determine if the gradient magnitude assumes a local maximum in the gradient direction.
Given vector fields and lying in the tangent bundle, the affine connection describes how to differentiate the vector field along the direction.
Given Bernal's Marxist and pro-Soviet sympathies it is perhaps remarkable that there has never been any suggestion that he fed any information in that direction.
Given the change in direction apparent in his poetry, scholars assume only his death a short time after publication prevented him from further exploration ; the collection may in fact have been published posthumously.
Given a unit vector u = ( u < sub > x </ sub >, u < sub > y </ sub >, u < sub > z </ sub >), where u < sub > x </ sub >< sup > 2 </ sup > + u < sub > y </ sub >< sup > 2 </ sup > + u < sub > z </ sub >< sup > 2 </ sup > = 1, the matrix for a rotation by an angle of θ about an axis in the direction of u is
Given an arbitrary direction z ( usually determined by an external magnetic field ) the spin z-projection is given by
Given charge of policy direction for the government in the latter role, he was often dubbed the " Minister for Thought " by the Press.
Given that v < sup > 2 </ sup > ignores direction, it is logical to assume that the formula can be extended to the entire sample, replacing m with the entire sample's mass, equal to the molar mass times the number of moles n yielding
Given a differential equation of the form ( for example, when F has zero slope in the x and y direction at F ( x, y ) ):
Given the abundance of these different guidance cues it was previously believed that growth cones integrate various information by simply summing the gradient of cues, in different valences, at a given point in time, to making a decision on the direction of growth.
Given the knowledge of the direction of the market we would ( potentially ) make a different investment vehicle decision.

Given and from
Given the absolute magnitude, for objects within our galaxy you can also calculate the apparent magnitude from any distance ( in parsecs ):
Given the absolute magnitude, you can also compute apparent magnitude from its parallax:
Given any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).
Given BASIC's straightforward nature, it was a simple matter to type in the code from the magazine and execute the program.
Love and Erlandson continued to pursue with the band, and released the single " Be A Man "— an outtake from the Celebrity Skin sessions — for the soundtrack of the Oliver Stone film Any Given Sunday ( 1999 ).
Given r, the rate of rotation is easy to infer from the constant angular momentum L, so a 2D solution can be easily reconstructed from a 1D solution of this equation.
Given two manifolds M and N, a bijective map f from M to N is called a diffeomorphism if both
Given the similarities between the rep proteins of the alphasatellites and the nanoviruses, it is likely that the alphasatellites evolved from the nanoviruses.
) Given a smooth Φ < sup > t </ sup >, an autonomous vector field can be derived from it.
Given that the vast majority of all emeralds are treated as described above, and the fact that two stones that appear visually similar may actually be quite far apart in treatment level and therefore in value, a consumer considering a purchase of an expensive emerald is well advised to insist upon a treatment report from a reputable gemological laboratory.
Given that genes are universal to living organisms, genetics can be applied to the study of all living systems, from viruses and bacteria, through plants and domestic animals, to humans ( as in medical genetics ).
Given two groups (< var > G </ var >, *) and (< var > H </ var >, ), a group isomorphism from (< var > G </ var >, *) to (< var > H </ var >, ) is a bijective group homomorphism from < var > G </ var > to < var > H </ var >.
Given a groupoid in the category-theoretic sense, let G be the disjoint union of all of the sets G ( x, y ) ( i. e. the sets of morphisms from x to y ).
Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G ( x, x ), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.
On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.
Given the Greek fleet's unpreparedness resulting from the premature outbreak of the war, such an early Ottoman attack might well have been able to achieve a crucial victory.
Given MLB's refusal to consider expansion, Kirksey, Cullinan, Smith, and Hofheinz joined forces with would-be owners from other cities and announced the formation of a new league to compete with the established National and American Leagues.
Given the opportunity to get away from the Sultan and visit new lands, he readily accepted.
Given earlier debates by Christian authors about the existence of Jesus, e. g. in Justin Martyr's 2nd century Dialogue with Trypho, it would have been expected that the passage from Josephus would have been used as a component of the arguments.
Given significant distance from the magnetic poles, one can figure which hand is which using a magnetic compass and the sun.
Given printing practices at the time ( which included type-setting from dictation ), no two editions turned out to be identical, and it is relatively rare to find even two copies that are exactly the same.
Given a year to complete the work, Gibson undertook the actual writing out of " blind animal terror " at the obligation to write an entire novel – a feat which he felt he was " four or five years away from ".

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