In some applications of vectors there is a need to move backwards and forwards between geometric form and component form; we deal here with how to achieve this.

To start with, we recall definitions of cosine and sine. If P is a point on the unit circle, and the line segment OP makes an angle Î¸ measured anticlockwise from the positive x-axis, then cosÂ Î¸ is the x-coordinate of P and sinÂ Î¸ is the y-coordinate of P (
Author(s): The Open University

I now want to take forward the notion of a science curriculum for public understanding, identifying problems and opportunities. Our guide in what follows is the Beyond 2000 document, which emerged from a working group led by UK-based science educators, working collaboratively with science teachers, education researchers, professional scientists within unive
Author(s): The Open University

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• What we must do to understand numbers as they are used as evidence in social science is to practise and so become familiar with them, and to understand the conventions which determine how they are used.

• Sets of numerical data can be presented in many ways, as tables, bar charts, pie charts or line graphs. These are just different ways of trying to represent or make a picture of numbers. Which is used is largely a matter of which best shows
Author(s): The Open University

The audio programme used in this unit addresses the issue of how arguments are constructed and used in the social sciences. It uses extracts from a radio programme (originally broadcast on BBC Radio 4 in January 1997) in which the social consequences of welfare provision are discussed from different viewpoints. The programme is organised to allow you to trace how arguments are being put together, assess what sort of assumptions are being made, and examine how forms of evidence are being used
Author(s): The Open University

Tables often give information in percentages. The table below indicates how the size of households in Great Britain changed over a period of nearly 30 years.

Number of people in household1961 (%)1971 (%)1981 (%)1991 (%)
1Author(s): The Open University

Look at Figure 9. Start with the map distance on the horizontal scale, move vertically up until you reach the line, then move horizontally until you reach the vertical axis. The number at that point will give you the corresponding ground distance in kilometres.

Author(s): The Open University

Capitalizing Works of Art
This video discusses how to properly capitalize the titles of works of art as well as artists' names.  It includes examples of correctly capitalized artists' names and works of art as well as incorrectly capitalized works and artists.  Audio can be hard to hear in sections of the video.

Author(s): No creator set

Mapping Wasps and Their Plant Hosts in Australia
Invertebrate Zoology Division Chair and Curator James Carpenter joins Dennis Stevenson of the New York Botanical Garden on an expedition to Australia in search of pollen wasps, their host plants, and the ways they might be adapted to each other. Along the way, they discover a new pollen wasp species, Paragia ozoe, and a plant family, Proteaceae, previously unknown to host wasp pollinators. The rare teaming of zoologist and botanist underscores the value of interdisciplinary collaboration and of
Author(s): No creator set

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Virtual Maths - 2D Shapes diagrams and formula
Diagram of 2D shapes, including formulas
Author(s): Leeds Metropolitan University

Working with dilemmas
Dilemmas are part of the fabric of organisational and individual life; these are often presented as the choice between two (or more) equally compelling propositions. In this free course, Working with dilemmas, you will focus on how to address dilemmas effectively. In particular, you will explore the extent to which dilemmas are or should be treated as choices between two extremes, and how the response to and resolution of dilemmas can move beyond binary choices to the reconciliation of opposites
Author(s): Creator not set

1.018J Fundamentals of Ecology (MIT)
This is a basic subject in ecology that seeks to improve the understanding of the flow of energy and materials through ecosystems and the regulation of the distribution and abundance of organisms. The course covers productivity and biogeochemical cycles in ecosystems, trophic dynamics, community structure and stability, competition and predation, evolution and natural selection, population growth and physiological ecology. There is particular emphasis placed on aquatic systems.

Author(s): Sallie Chisholm,Laurel Schaider

2.003J Dynamics and Control I (MIT)
This class is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics include kinematics; force-momentum formulation for systems of particles and rigid bodies in planar motion; work-energy concepts; virtual displacements and virtual work; Lagrange's equations for systems of particles and rigid bodies in planar motion; linearization of equations of motion; linear stability analysis of mechanical systems; free and forced vibration of linear multi-deg
Author(s): Makris, Nicholas,So, Peter,Sarma, Sanjay,Modarres-

We have seen in Section 2.2 that the complex number system is obtained by defining arithmetic operations on the set RÂ Ã—Â R. We also know that elements of RÂ Ã—Â R can be represented as points in a plane. It seems reasonable to ask what insight can be obtained by representing complex numbers as p
Author(s): The Open University

Tips to keep kids interested in reading during the summer months. (01:21)
Author(s): No creator set

Meat Porters (1959) by Ralph Brown, Market Square, Town Centre, Harlow, Essex. General view from the south west. Photographed by Steven Baker 2015.

Author(s): No creator set

Mammals share a number of biological characteristics that mark them out as members of the class Mammalia. Many of these are adaptations to a life on land. For example:

• Mammals give birth to young at a relatively advanced stage of development and feed their young on milk.

• Most mammals have hair, or fur, covering part or all of the body.

• Mammals have a high metabolic rate and maintain a relatively high and constant body temp
Author(s): The Open University

After studying this course, you should be able to:

• describe the geological history of the Scottish Highlands

• give examples of igneous, metamorphic and structurally complex rocks.

Author(s): The Open University

Review response to water quality problems
This learning object contains resources and activities that focus on reviewing a response to a water quality problem. The key areas are: reviewing the incident and completing the documentation requirements. The task is to investigate and evaluate the response and record your findings.
Author(s): No creator set