How Would You describe Greenland's Tundra?
Interview on physical composition and social science attributes of Greenland’s tundra, including teacher’s personal observations from this polar region. Run time 02:28.
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The Royal Family Tree : Oefening op familierelaties
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Deze oefening bevat een beknopte stamboom van de huidige Britse royal family; Koningin Elizabeth II en haar kinderen, kleinkinderen en achterkleinkinderen.

Onderaan staan er enkele invulzinnen om de woordenschat van de familierelaties in te …


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2.6 Line symmetry

Look at the shapes below. The symmetry of the shape on the left and its relationship to the shape on the right can be thought of in two ways:

  • Fold the left-hand shape along the central line. Then one side lies exactly on top of the other, and gives the shape on the right.

  • Imagine a mirror placed along the central dotted line. The reflection in the mirror gives the other half of the shape.

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Keep on learning

Study another free course

There are more than 800 courses on OpenLearn for you to choose from on a range of subjects. 

Find out mo
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James Bamford on the National Security Agency

James Bamford talks to Nathan Thrall about the politics behind the Bush administration's evasion of the Foreign Intelligence Surveillance Act and the technology and scope of the National Security Agency's warrantless wiretapping program.


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1.7 Geological fieldwork

Although much can be learned from samples of rocks in the laboratory or at home, the ‘natural habitat’ of rocks is outdoors. Here the distribution and layout of different rocks is visible wherever rocks are exposed in places such as stream beds, cliffs, rocky shorelines, quarries, or road cuttings. The exposed rocks can be studied in just the same detail as individual laboratory samples, and geological fieldwork allows the size and extent of each rock unit to be seen and the relationships
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1.6 Interlude

Now that we have covered the features found in igneous, sedimentary and metamorphic rocks, and seen how these features can be explained by the processes that formed the rocks, here is a useful point at which to have a break before continuing with the next section. Before returning, you might like to see for yourself what types of rock you can find in your area. Can you identify their texture, or spot any fossils? Surfaces that haven't been obscured by grime or lichens are by far the best, as
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1.4.5 Fossils and ancient environments

An essential component of any environment is the plant and animal life that is adapted to the prevailing conditions. Fossil plants and animals are therefore wonderful sources of information about ancient environments. Plants can leave behind remains ranging from roots, leaves and twigs to seeds and pollen. Leaves and twigs are relatively fragile, and require a comparatively low energy environment (e.g. the mudflats of an estuary) for their preservation. Seeds, pollen and spores are surprising
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4.2 Earthquake magnitude

The magnitude of an earthquake is a measure of the amount of seismic energy released by it, so it is a quantitative scale. The scale of earthquake magnitude is called the Richter scale. Its development is described in Box 4, Charles Richter and the Richter earthquake magnitude scale. The Richter magnitude is calc
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Introduction

This course is concerned with two main topics. In Section 1, you will learn about another kind of graphical display, the boxplot. Boxplots are particularly useful for assessing quickly the location, dispersion, and symmetry or skewness of a set of data, and for making comparisons of these features in two or more data sets. The other topic, is that of dealing with data presented in tabular form. You are, no doubt, familiar with such tables: they are common in the media and in reports an
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2.1.2 Try some yourself

Activity 15

Suggest appropriate units for each of the following:

  • (a) the age of the kitten when it is weaned;

  • (b) the distance between one train station and the
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2.10 The complex exponential function

Consider the real exponential function f (x) = ex (that is, f (x) = exp x). We now extend the definition of this function to define a function f(z) = ez whose domain and codomain are Author(s): The Open University

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Learning outcomes

After studying this course, you should be able to:

  • understand the arithmetical properties of the rational and real numbers

  • understand the definition of a complex number

  • perform arithmetical operations with complex numbers

  • explain the terms modular addition and modular multiplication

  • explain the meanings of a relation defined on a set, an equivalent relation and a partition of a set.


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Acknowledgements

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

Course image: Stuart Rankin in Flickr made available under Creative Commons Attribution-NonCommercial 2.0 Licence.

All materials included in this course are
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Learning outcomes

After studying this course, you should be able to:

  • create simple models, given a clear statement of the problem

  • identify the simplifying assumptions that underpin a model

  • identify the key variables and the parameters of a model

  • apply the input–output principle to obtain a mathematical model, where appropriate.


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2.8 The angles of a triangle

The sum of the angles of any triangle is 180°. This property can be demonstrated in several ways. One way is to draw a triangle on a piece of paper, mark each angle with a different symbol, and then cut out the angles and arrange them side by side, touching one another as illustrated.


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Try some yourself

Question 1

Draw a line of symmetry on each of the shapes below.

2.7 Rotational symmetry

There is another kind of symmetry which is often used in designs. It can be seen, for instance, in a car wheel trim.

Look at the trim on the left. It does not have line symmetry but
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1.4 Parallel lines

Two straight lines that do not intersect, no matter how far they are extended, are said to be parallel. Arrows are used to indicate parallel lines.


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1.3.4 Vertically opposite angles

When two straight lines cross, they form four angles. In the diagram below, these angles are labelled α, β, θ and φ and referred to as alpha, beta, theta and phi. The angles opposite each other are equal. They are called vertically opposite angles. Here α and β are a pair of vertically opposite angles, as are θ and φ. Although such angles are called ‘vertically opposite’, they do not need to be vertically above and bel
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