Experiments or surveys usually generate a lot of information from which it is possible to draw conclusions. Such information is called data. Data are often presented in newspapers or books.

One convenient way to present data is in a table. For instance, the nutrition panel on the back of a food packet:

### Nutrition Information

Author(s): The Open University

## Exercise 1

A vector a has magnitude |a|Â =Â 7 and direction Î¸Â =Â âˆ’70Â°. Calculate the component form of a, giving the components correct to two decimal places.

<
Author(s): The Open University

The displacement from a point P to a point Q is the change of position between the two points, as described by the displacement vector

If P and Q represent places on the ground, then it is natural to use a bearing to describe the direct
Author(s): The Open University

In the following subsections, we apply the vector ideas introduced so far to displacements and velocities. The examples will feature directions referred to points of the compass, known as bearings.

The direction of Leeds relative to Bristol can be described as â€˜15Â° to the East of due Northâ€™, or NÂ 15Â°Â E. This is an instance of a bearing. Directions on the ground are typically given like this, in terms of the directions NorthÂ (N), SouthÂ (S), EastÂ (E)
Author(s): The Open University

The following activity illustrates how the conversion processes outlined in the preceding sections may come in useful. If two vectors are given in geometric form, and their sum is sought in the same form, one approach is to convert each of the vectors into component form, add their corresponding components, and then convert the sum back to geometric form.

Author(s): The Open University

You have seen how any vector given in geometric form, in terms of magnitude and direction, can be written in component form. You will now see how conversion in the opposite sense may be achieved, starting from component form. In other words, given a vector aÂ =Â a 1 iÂ +Â a 2 j, what are its magnitude |a| and direction Î¸?

The first part of this question is dealt with using Pythagorasâ€™ Theorem: the magnitude of a v
Author(s): The Open University

All materials included in this unit are derived from content originated at the Open University.

Author(s): The Open University

Assuming that both the content of mathematics and the processes need to be included in programmes and curricula, the problem becomes one of how a suitable curriculum can be structured. One possibility is to construct a very specific curriculum with clearly defined objectives for both content and processes separately, and possibly with suggested learning activities. However, content and process are two complementary ways of viewing the subject.

An alternative is to see the curriculum in
Author(s): The Open University

This unit is aimed at teachers who wish to review how they go about the practice of teaching maths, those who are considering becoming maths teachers, or those who are studying maths courses and would like to understand more about the teaching process.

This unit is from our archive and is an adapted extract from Teaching mathematical thinking at Key Stage 3 (ME624) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other cour
Author(s): The Open University

RSS (â€˜Really Simple Syndicationâ€™ or â€˜Rich Site Summaryâ€™) newsfeeds supply headlines, links, and article summaries from various websites. By using RSS â€˜feedreaderâ€™ software you can gather together a range of feeds and read them in one place: they come to you, rather than you having to go out and look for breaking news. The range of RSS feeds on offer is growing daily. There is probably a feed to cover all aspects of your life where you might need the latest information, and you may
Author(s): The Open University

Referencing is not only useful as a way of sharing information, but also as a means of ensuring that due credit is given to other peopleâ€™s work. In the electronic information age, it is easy to copy and paste from journal articles and web pages into your own work. But if you do use someone elseâ€™s work, you should acknowledge the source by giving a correct reference.

Taking someone's work and not indicating where you took it from is termed plagiarism and is regarded as an infringemen
Author(s): The Open University

If you are considering taking your studies further you might like to consider using bibliographic software. Bibliographic software can be used to sort references, annotate them, manage quotations or create reading lists.

There are several software packages on the market. Some are listed below.

• BibTex

• EndNote

• Procite

• Reference Manager

• RefWorks

If you are not sure
Author(s): The Open University

• 87% of items that are filed into a filing cabinet are never looked at again. STANFORD UNIVERSITY

• The world is producing nearly two exabytes of new and unique information every year â€“ an exabyte is a new term that had to be coined for a billion gigabytes. All the words ever spoken by human beings comes to five exabytes. UNIVERSITY OF CALIFORNIA (BERKELEY)

• More new information has been produc
Author(s): The Open University

The second argument is more profound: long-term profitability, and the existence of business itself, is threatened if companies can't transform themselves. This assumes that although the costs of environmental and social impacts can be ignored for a period, in the context of globalisation of environmental, social and political processes, they will come back to haunt businesses, and ultimately threaten their survival. There are several communications and management tools that have been develop
Author(s): The Open University

Where will the decisions be made that will result in meaningful action on climate change, and who will make them stick? Following climate change politics in the media can give the impression that most of the action on climate change is going on between national decision makers in international forums. It is important to keep in mind that these forums have resulted from persistent pressure from a combination of grassroots environmental activists and a global network of science and policy exper
Author(s): The Open University

In this part I have presented evidence showing that even apparently remote regions of our planet are intimately connected through physical processes. For example, once an organic POP is transported to the poles, then biological processes can take over and through bioaccumulation perhaps cause harm. But this physical connection has allowed the ice to preserve unique proxy records of the past climate of our planet. Directly measuring the gases trapped in the ice has enabled histories of past at
Author(s): The Open University

Greenland snowfall differs depending on whether it falls in summer (when snow is comparatively warm and moist) or winter (when snow is cold and dry). These differences mean that as the snow is turned to ice, annual layers are formed that are in many ways similar to tree rings: thick annual layers mean high snowfall and thin annual layers low snowfall. The accumulation of snowfall on the summit of Greenland â€“ and most importantly what is trapped within the crystals as it turns to ice â€“ can
Author(s): The Open University

The scientific theory of plate tectonics suggests that at least some of these Arctic lands were once tropical. Since then the continents have moved and ice has changed the landscape. This unit will concentrate on evidence from the last 800,000 years using information collected from ice cores from Greenland and Antarctica, and will use this evidence to discuss current and possible future climate. The cores show that there have been nine periods in the recent past when large areas of the Earth
Author(s): The Open University

Despite all the possibilities for individual and group action to lighten carbon footprints, there will still be people, groups and organisations who will not be doing much. Many individuals limit themselves to â€˜every little bit helpsâ€™, with relatively minor effects on their carbon footprint, like reusing plastic bags or recycling paper. This avoids having to consider more significant changes in car and air travel, home energy use, diet or shopping. Others will simply carry on producing an
Author(s): The Open University

Let's now look at carbon footprint reduction targets in a bit more detail.

The first international agreement to set carbon reduction targets was the 1997 United Nations Kyoto Protocol, which requires developed countries to reduce their human-generated greenhouse gas emissions by an average of just over 5% on 1990 levels by 2008 to 2012. By the time the treaty came into force in 2005, only the USA and Australia had refused to sign. (A new Australian government finally signe
Author(s): The Open University