Maths Notes Maths Notes for Shear and Stretch Stretch • The transformation consists of:o o • The invariant line Scale factor For stretch‚ the transformation takes place perpendicular to the invariant line. • Scale factor(K) = 4 3 2 1 -2 -1 0 -1 -2 -3 1 2 3 = Y 4 X Invariant line In the above example‚ the x-axis is the invariant line and the object lies on (1‚1). Thus‚ =1 The scale factor is given to us as K = 3 1 Maths Notes Thus‚ acc. to the formula given
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As some of my peers might know‚ geometry is definitely not my favorite subject in math. I have always struggled with geometry‚ especially with memorizing formulas to solve problems such as finding volume‚ surface area and more. I always found formulas to be such a bother and even after learning one and mastering it somewhat‚ I usually ended up forgetting the formula. Fortunately‚ the formulas that I had the most trouble with‚ being volume‚ surface area‚ and area‚ have finally began to stick with
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in the document.) After completing the molecular models‚ fill in the table below: (18 points) Molecule What is the central atom of this molecule? Number of lone pairs on the central atom Number of atoms bonded to the central atom Molecular geometry Bond angle (based on VSEPR theory) CCl2F2 C Zero 4 Tetrahedral 109 degrees HCN C Zero 2 Linear 180 degrees H2O O Two 2 Linear Bent 109 degrees NH3 N One 3 Trigonal Planar 109 degrees H2S S
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dominant method of communication‚ will have power over the common person. Take the Second World War‚ for example. Words were being used by all sides to manipulate their own people to support national ideas. Perhaps the most notable example of this manipulative phenomenon is Nazi Germany. In Mein Kampf‚ Adolf Hitler‚ who would become the dictator of the Third Reich‚ accused the Jewish people of the world of using fabrications
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shows that Pierre de Fermat (1601-1665)‚ also a French mathematician and scholar‚ did more to develop the Cartesian system than did Descartes. The development of the Cartesian coordinate system enabled the development of perspective and projective geometry. It would later play an intrinsic role in the development of calculus by Isaac Newton andGottfried Wilhelm Leibniz.[3] Nicole Oresme‚ a French philosopher of the 14th Century‚ used constructions similar to Cartesian coordinates well before the time
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Molecular Geometry A. Natural Orientation of Volumes about a Central Point. You will need 20 round balloons for this experiment. Join them together as indicated in the Balloon Arrangement column and then describe the shape in the space provided. Balloon Arrangement Description of the Shape Two-Balloon Set Linear Three-Balloon Set Trigonal Planar Four-Balloon Set Tetrahedral Five-Balloon Set Trigonal Bipyramidal Six-Balloon Set Octahedral B. Valence Shell Pairs: Single
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Theorems 1 All right angles are congruent. 2 Perpendicular lines form right angles. 3 If two angles are complements or supplements to the same or congruent angles‚ they are congruent. 4 Two adjacent angles that fall on the same line form a linear pair and are supplementary. 5 Corresponding parts of congruent triangles are congruent. 6 If two sides of a triangle are congruent the angles opposite are congruent. 7 If two angles in a triangle are congruent the sides opposite are congruent. 8 The base
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Christopher Lothman Geometry Distance Formula: Translation A’ (10‚ 1) B’ (2‚ 1) C’ (2‚ 7) Rule: (x‚ y) > (x 8‚ y + 4) A2C2 = sqrt(((2 (10))^2) + ((7 1)^2)) = 10 AC = sqrt(((6 (2))^2) + ((3 (3))^2)) = 10 A2C2 = AC A2B2 = sqrt(((2 (10))^2) + ((1 1)^2)) = 8 AB = sqrt(((6 (2))^2) + ((3 (3))^2)) = 8 A2B2 = AB B2C2 = sqrt(((2 (2))^2) + ((7 1)^2)) = 6 BC = sqrt(((6 6)^2) + ((3 (3))^2)) = 6 B2C2 = BC Triangle A2B2C2 = Triangle ABC by construction
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lone pairs over the central atom in POCl3 are [WB JEE 2012] (A) sp‚ 0 (B) sp2‚ 0 (C) sp3‚ 0 (D) dsp2‚ 1 Answer: (C) 2. NiCl2{P(C2H5)2(C6H5)}2 exhibits temperature dependent magnetic behaviour (paramagnetic/diamagnetic). The coordination geometries of Ni2+ in the paramagnetic and diamagnetic states are respectively [IIT JEE 2012] (A) tetrahedral and tetrahedral (B) square planar and square planar (C) tetrahedral and square planar (D) square planar and tetrahedral Answer: (C) 3. When
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chemistry department. He moved to Canada in 1958‚ where he became a professor at McMaster University in Hamilton‚ Ontario. Developed in 1957 with Ronal Nyholm‚ Gillespie has done extensive work on expanding the idea of the VSEPR model of molecular geometry. The theory they created is much more effect to predict‚ explain and describe the 3D molecular shapes (linear‚ pyramidal‚ cubical etc.) based on the number of electron pairs that are found on the outer shell. Their theory is based on electron repulsion
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