The AnglE model introduces angle optimization to address common challenges like vanishing gradients and underutilization of supervised negatives in Large Language Models (LLMs). By enhancing the gradient and optimization processes, this novel approach improves text embedding learning effectiveness.

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Discover how to solve right triangles using trigonometric ratios and angle measures. Explore examples and real-world applications, such as calculating street grades in San Francisco. Learn how to identify angles using sine, cosine, and tangent ratios, and use inverse trigonometric functions to find

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Prisms are optical devices that deviate light without changing its vergence. This module explores the various terminology associated with prisms, including Apex, Base, Refracting Angle, and Angle of Deviation. The passage of light through a prism follows Snell's Law, where the ray is deviated toward

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Fresnel prisms, a type of prism where the angle of refraction only depends on the surface angle and material's refractive index, offer advantages such as thinness, lightweight, and flexibility but have disadvantages like cosmetic differences and reduced visual performance. They find applications in

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Explore key geometry vocabulary such as congruent, vertical, adjacent, complementary, and supplementary angles. Learn how to identify different types of angle pairs and calculate unknown angle measures using angle relationships. Visual examples and explanations enhance understanding.

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Detailed instructions on how to operate a Kruss goniometer contact angle analyzer. Learn how to set up the equipment, prepare the sample, adjust camera focus, measure contact angle, and analyze the results. Follow each step carefully to achieve accurate measurements.

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Glaucoma, the 3rd leading cause of blindness in Uganda, is primarily managed by General Ophthalmologists across 20 hospitals in the country. Uganda lacks Glaucoma subspecialists and specialized nurses. Equipment availability varies among hospitals. Cases in Uganda are typically identified through re

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Learn how to rotate shapes around a center by a specified angle and describe the resulting transformation. Explore concepts like center of rotation, angle, and sense of rotation. Practice rotations with various examples and understand the process step by step.

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In this educational material, students will learn to differentiate between acute, right, and obtuse angles. They will practice identifying angles, ordering them from smallest to largest, and determining angles within various shapes. The content also includes reasoning exercises to enhance understand

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This strand delves into trigonometric problems focusing on triangles with mixed information, exploring side lengths and angle measurements beyond right-angled triangles. It covers mixed problems, sine and cosine rules, applying area of any triangle, and Heron's formula. Engage in various exercises i

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Explore the Vocabulary of Exterior Angle Inequality Theorem, Angle-Side Relationship Theorems 5.9 and 5.10. Understand how to order triangel angle measures and side lengths from smallest to largest through examples. Discover the principles governing triangles in terms of angles and side lengths.

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This content explains the concept of exterior angles in polygons and the Exterior Angle Theorem. It covers how exterior angles are formed when the sides of a polygon are extended, their relationship with interior angles, and how to calculate their measures using the Exterior Angle Theorem. Various e

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Explore the EmPower Oarlock and SpeedCoach GPS systems for rowing, providing real-time feedback on stroke metrics like length, blade engagement, and force. Customize your display with various metrics and receive technical feedback on improving catch angle, finish angle, blade engagement, and more. E

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Photography is a form of art that involves various creative expressions, including the use of different camera angles to capture unique perspectives. This content explores different camera angles such as high-angle shot, low-angle shot, Dutch angle, and straight angle, each offering a distinct visua

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Overview of Dp-branes, NS5-branes, and U-duality derived from nonabelian (2,0) theory with Lie 3-algebra. Introduction to M-theory, including M2-branes and M5-branes in the strong coupling limit. Discussion on BLG theory, Lorentzian Lie 3-algebra, and the ABJM theory for M2-branes.

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Learn about the correct usage of transitive and intransitive verbs with examples of common verb pairs like lie/lay, sit/set, and rise/raise. Understand the distinctions between these verb forms to improve your grammar skills and communication accuracy. Enhance your knowledge through this detailed le

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This supplemental content presents comparisons of dyslipidaemia, final minimal luminal diameter (MLD), distance between ostium of the LAD and proximal edge of the stent, lesion length, and various angle measurements in different restenosis groups. The findings highlight significant differences in dy

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This briefing delves into the potential physical and infrastructure effects of an impact event with an asteroid of up to 400 meters in diameter, traveling at a speed of 16 km/s. The simulation highlights the significant threat of tsunamis resulting from such an impact, with tsunami strength varying

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When purchasing a hockey stick, it goes beyond just color or brand name. Understanding factors like lie angle, flex, and curve pattern is crucial for optimal performance. The lie angle determines how much blade is on the ice, impacting handling and shooting. Flex and length also play key roles in fi

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Delve into the world of triangles in geometry with a focus on classifying them by their sides and angles. Learn about equilateral, scalene, and isosceles triangles based on side lengths, and explore equiangular, right, acute, and obtuse triangles according to angle measurements. Uncover the Triangle

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Delve into the principles of congruent triangles by exploring the properties of side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), and right-angle-hypotenuse-side (RHS) congruence. Visual explanations help clarify how these properties determine if triangles are congruent.

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Explore the concepts of perpendicular and angle bisectors in triangles through visuals and theorems. Learn how to identify, utilize, and apply these bisectors to solve problems involving segments and angles within triangles. Enhance your understanding of bisectors with examples and step-by-step expl

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Explore practice questions demonstrating the similarity of triangles based on angle relationships. Understand how to prove similarity using given angle measurements in various triangle configurations. Delve into the concept of similar triangles through visual examples and step-by-step solutions.

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Explore the concept of angle relationships created by intersecting lines and transversals. Learn about linear pairs, congruent angles, supplementary angles, alternate interior and exterior angles, corresponding angles, and more. Engage in activities, quizzes, and worksheet assignments to deepen your

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Polar coordinates define the location of a point in terms of distance and angle from an origin. The distance is denoted by "r" and the angle by "?". However, the angle is not unique for a point. The concept involves fixing an origin and an initial ray, with positive angles measured counterclockwise.

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Polar coordinates provide an alternative way to plot points using a directed angle and distance from the origin. This system involves radius (distance) and angle measurements, allowing for multiple representations of points. Graphing polar coordinates, converting between polar and rectangular coordi

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Learn the distinction between the transitive verb "lay" and the intransitive verb "lie" in English grammar, along with their principal parts and usage examples. Avoid confusion by understanding when to use "lay" and "lie" correctly in different contexts.

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In this lesson on additive angle measures, students learn how to find missing angle measures when two non-overlapping angles combine to form a larger angle. Essential questions are posed, and students are guided through solving problems involving angle decomposition and measurement. Practical activi

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Explore the concepts of equidistance and angle bisectors in geometry through practical examples like determining the path for John to walk equidistant from a hedge and a wall, understanding the ideal flight path for a plane to land, constructing angle bisectors, and verifying constructions for accur

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Dive into the world of geometry with various diagrams and scenarios focusing on angle sums, concave and convex polygons, and angle measurements. Learn about properties of polygons and test your skills in identifying different shapes and their classifications based on their properties. Explore angles

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A delightful story of a puppet and a mouse, teaching children the importance of honesty and forgiveness. When a simple lie causes a rift between them, the power of apologies and kindness leads to a beautiful friendship. Illustrated by Zanthe Goedhals, this story emphasizes the value of truthfulness

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Explore the application of angle-pair theorems in finding missing angle measures using properties of parallel lines. Learn about different types of angle pairs such as vertical angles, corresponding angles, same-side interior angles, alternate exterior angles, and more through engaging activities an

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Explore the world of angles with definitions of angle parts, types of angles, angle pairs, Angle Addition Postulate, and more. Dive into examples and classwork exercises to enhance your understanding of angles in geometry.

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Learn how to apply angle pair theorems using properties of parallel lines to find missing angle measures. Explore concepts like corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles through visual aids and practice problems.

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Explore key facts about the American West history through a fun game of "Three Truths and a Lie." Learn about the Homestead Act, Plains Indians, cattle ranching, the Open Range, policing in the West, early settlers, and farming innovations. Test your knowledge and uncover the true from the false in

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Explore the Polygon Angle-Sum Theorems that determine the sum of interior angle measures in polygons. Learn about the Polygon Angle-Sum Theorem, number of sides in polygons, finding angle sums, and the corollary for regular polygons. Practice using the theorems to calculate interior angle measures i

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This content delves into understanding triangle congruence and similarity through various scenarios and visual representations. It discusses how to determine congruence using side-side-side, side-angle-side, and angle-side-angle criteria, and explores the concept of similarity in triangles based on

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Learning about parallel lines involves using angle facts like those on a straight line or around a point. By interpreting what a transversal is, you can apply angle relationships such as corresponding, alternate, co-interior, and vertically opposite angles. Practice finding unknown angles and identi

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Glaucoma is a group of eye conditions that can lead to irreversible vision loss. There are different types such as open-angle, closed-angle, secondary, and normal-tension glaucoma, each with unique characteristics and causes. Symptoms vary from rapid damage in closed-angle glaucoma to gradual periph

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Framing Riemannian Geometry as a Generalized Lie Algebra to combine General Relativity with Quantum Theory. The proposal extends Heisenberg Algebra to incorporate a more general geometry, allowing for a function of position in commutator relationships. The discussion covers historical developments,

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