Plans of houses and instructions for assembling shelves, etc., often come in the form of scale diagrams. Each length on the diagram represents a length relating to the real house, the real shelves, etc. Often a scale is given on the diagram so that you can see which length on the diagram represents a standard length, such as a metre, on the real object. This length always represents the same standard length, wherever it is on the diagram and in whatever direction.

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

On completion of this unit you should be able to:

• convert a vector from geometric form (in terms of magnitude and direction) to component form;

• convert a vector from component form to geometric form;

• understand the use of bearings to describe direction;

• understand the difference between velocity and speed;

• find resultant displacements and velocities in geometric form, via the use of components.

Author(s): The Open University

Two activities are given below. You are asked to work on them in turn and to record not only your working, but observations on what you notice about your emotions as you work through step by step.

## Activity 3 Constrained numbers

W
Author(s): The Open University

Working in mathematics education involves a sense of both past and future, and how the two combine to influence the present. It may seem that, because the past has already happened, it cannot be altered; however, you can alter how you perceive the past, and what lessons you take from it. Each of us has a personal past in mathematics educationâ€”the particular events of our personal lives, who taught us, where, what and how they taught us, and what we took from the experiences. Each of us also
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

We mentioned above that we need to reference sources to ensure we abide by copyright legislation. But there is another reason we need to give accurate references to items we use â€“ so we can share it.

Consider this scenario. A friend says theyâ€™ve just read an interesting article where Joshua Schachter, founder of del.icio.us has spoken about why it isnâ€™t a faceted search system, and you should read it. How would you go about finding it? Would you start looking in a news database, a
Author(s): The Open University

Question 1

Although most people immediately think of economic globalisation, Section 1 shows how political, social/cultural and ecological globalisation are also significant in the context of global environmental change.

Question 2

The advocates of â€˜business learnsâ€™ are optimistic about the global free-market civilisation they believe they are building, but they also believe business needs to heed environmental and social concerns for its own sake. â€˜Radic
Author(s): The Open University

Communities such as Findhorn already behave as if natural resources need careful management: they work hard to reduce fossil fuel use. A central assumption of this way of thinking is that people need to root economies more locally (Figure 15). To see the same impulse spread through the mainstream economy would require that th
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

Business can profit from taking the environment into account (generally called eco-efficiency). Poor environmental performance is seen as a reflection of poor business practice in general. Eco-efficiency promotes the economic benefits of energy and materials savings, at the same time being first to market with new technologies or products. Since business sustainability lobbies promoted eco-efficiency in the early 1990s, the creed has gained rapid acceptance, and with good cause. There
Author(s): The Open University

Business can learn to integrate ecological thinking into the core of its thinking and become the hub of a sustainable society. This is the claim of the business learns position. As environmentalists have spent over 30 years portraying business as the arch-villain of the piece, this is a grand claim. One of the people who have stated it most clearly is Ray Anderson, head of the US carpet giant Interface (Author(s): The Open University

Governance is from the Greek words kybenan and kybernetes, meaning â€˜to steerâ€™ and â€˜pilotâ€™ or â€˜helmsmanâ€™. It is the process whereby â€˜an organization or a society steers itself, and the dynamics of communication and control are central to the processâ€™ (Rosenau and Durfee, 1995, p. 14). Of course, you could read these words as a pretty sound definition of government but that would be missing the point. Government describes a more rigid and narrower set
Author(s): The Open University

Alley, R. B. (2000) The Two Mile Time Machine, Princeton, Princeton University Press.
Arnakak, J. (2000) â€˜What is Inuit Qaujimajatuqangit?â€™, Nunatsiaq News, 25 August, p. 11.

Author(s): The Open University

The Keeling curve is the plot showing the trend in rising atmospheric CO2 concentrations since 1958 recorded at Mauna Loa in Hawaii. The story of atmospheric CO2 in the last 50 years is a relentless rise derived from human use of hydrocarbons and, as I write this in 2008, the annual mean concentration is 383 parts per million (ppm). When Keeling first collected his CO2 data he travelled around making the measurements at widely spaced locations â€“ but he saw t
Author(s): The Open University

Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

The content acknowledged below is Proprietary and used under licence (not subject to Creative Commons licence). See Terms and Conditions.

## Unit image

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Author(s): The Open University

Few people agree that individuals should take the main responsibility for tackling environmental issues. For example, in a 2007 poll of over 2000 UK citizens, 70% agreed that the government should take a lead in combating climate change, even if it means using the law to change people's behaviour. However, over 60% disagreed that there was nothing they could do to avert climate change and over half agreed that they would do more if others did more too, although 40% thought that recycling was
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

This unit focuses on the problem of greenhouse gas emissions, especially carbon dioxide, and explore what you can do to lighten those emissions to help reduce the rate of climate change. You will assess your â€˜carbon footprintâ€™ and see what actions you and, if relevant, other household members could take to lighten that footprint. You will also better understand which actions are more and less effective, and the scope and limits of what individuals can do at the personal and household leve
Author(s): The Open University

The observed increase in GMST may be the key global indicator of greenhouse warming, but it is far from being the only tangible sign of climate change during the 20th century. This brings us back to the first bullet point at the beginning of Section 2.1. Here, we take a brief look at the growing body of evidence that many different climate variables, as well as physical and biological systems around the world, have been affected by recent climate warming. The examples collected in Box 9 will
Author(s): The Open University